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Subject. Organisational and regulatory peculiarities of the regional system of remuneration of healthcare workers in state medical organisations. Purpose. This study aims to analyse the current system of remuneration of healthcare workers of state healthcare institutions in the Voronezh Region, to identify current issues, and to determine the main paths for improving the sectoral remuneration system. Method. The study used data from statistical reports related to the structure and composition of wages in 2019-2020 and other financial indicators of the healthcare system in the Voronezh Region. The methods of the investigation included analysis, observation, generalisation, comparison, grouping, classification, etc. Results. A method for calculating the amount of guaranteed payments was offered, the earlier and current remuneration systems were compared. The analysis of wage systems in medical organisations subordinate to the Department of Health of the Voronezh Region confirmed the need to increase the basic salary and reimbursements in order to improve the welfare of healthcare workers, which contributes to improving the quality and accessibility of medical care. Conclusions. The hypothesis was confirmed that it is necessary to develop a concept and methodological recommendations for the formation of a sectoral remuneration system containing information on the amount of salaries, the key approaches to determining reimbursements and incentive payments and their ratio in order to decrease the differentiation between healthcare workers’ salaries in the region and to increase the appeal of the profession and to motivate employees to work more efficiently.

The problem of achieving a higher level of ductility of pipe steels of strength grades K60 (X70) and K65 (X80) is described. Results of laboratory and industrial experiments are shown, and requirements for pipe microstructure with improved deformation capacity are formulated. Technology is described providing the specified type of structure and steel target mechanical properties, and different production schemes for LTCC are applied making it possible to achieve the prescribed strength and ductility properties over a wide variation range. Results are provided for mass industrial production of rolled product and pipe with high deformation capacity.

Предмет. Организационные и методические аспекты ведомственного контроля финансового-хозяйственной деятельности и других видов ведомственного контроля, осуществляемых исполнительными органами власти в отношении подведомственных учреждений. Цель. В исследовании поставлена цель определить место ведомственного контроля финансово-хозяйственной деятельности в системе финансового контроля Российской Федерации, изучить действующие организационные модели отдельных видов ведомственного контроля на примере системы государственного здравоохранения Воронежской области, определить проблемные вопросы и предложить возможные варианты их решения. Метод. В процессе исследования использовались данные консолидированного бюджета РФ и бюджетов государственных внебюджетных фондов РФ за 2020 г., консолидированного бюджета государственных медицинских организаций Воронежской области и другие финансовые показатели системы здравоохранения Воронежской области за аналогичный период. Применялись методы анализа, наблюдения, обобщения, сравнения, группировки, классификации и др. Результаты. Разработана организационная структура контроля (надзора) в сфере охраны здоровья и финансового контроля сферы государственного здравоохранения, исследованы полномочия и функции исполнительных органов власти. Анализ основных разделов контрольных видов выявил взаимосвязь внешнего и внутреннего контроля как элементов единой системы контроля. Приведены примеры типичных нарушений, выявленных по результатам ведомственного государственных медицинских организаций Воронежской области. Выводы. Подтверждена гипотеза о необхомости осуществления ведомственного контроля финансового-хозяйственной деятельности, как части системы государственного (муниципального) управления, посредством инструментария финансового контроля и учетом отраслевой специфики.

The comparative effect of molybdenum and chromium on critical points, structure and strength properties of low-carbon pipe steel after different cooling regimes is studied. It is shown that for the basic chemical composition 0.06%C–1.50% Mn–Cu–Nb–Ti addition of chromium and molybdenum leads to a reduction in Ar3 and Bs critical points for hot-worked austenite decomposition. It is noted that with use of the optimum accelerated cooling regime the difference is overcome between the effect of molybdenum and chromium on dispersion of the structure and strength properties of low-carbon pipe steel of the alloy system 0.06% C–1.50% Mn–Cu–Nb–Ti.

A study was conducted concerning the kinetics of phase transformations and structure of grade K60 (X70) pipe steels alloyed with small amounts of chromium (K60Cr) and molybdenum (K60Mo). It was shown that K60Mo steel differs by a higher structural content of M/A components. The laboratory tests and microstructure studies of the obtained samples by color etching, TEM, and XRD methods have shown that by using the improved cooling conditions after thermomechanical rolling of K60Cr steel, it becomes possible to obtain samples having different matrix microstructure (polygonal, quasi-polygonal, or bainitic ferrite) and various secondary phases (M/A or cementite), which yields different mechanical properties ranging from 467 to 633 MPa (yield point – σy ); 681 to 804 MPa (ultimate strength – σt ); 22 to 31.8% (percent elongation – δe); 8.8 to 17.4% (proportional elongation – δp); and 0.68 to 0.88 (σy /σt ratio). It was established that the presence of M/A component instead of cementite in the structure contributes to an increase in strength and decrease in σy /σt ratio without a considerable decline in cold resistance. At JSC “Vyksa Metallurgical Plant” (VMZ), K60Cr steel, which is more economical compared to K60Mo, and newly developed technology were used to produce commercial batches of rolled products and large diameter pipes, which demonstrated the specified σy /σt ratio and higher impact toughness and cold resistance values during a drop weight tear test (DWTT).

The influence of various etching processes on the single-crystalline (100) silicon surface is studied. It is demonstrated that microstructuring of the surface of high-resistivity single-crystalline silicon in alkaline solutions is better performed using electrolytic methods at temperatures no lower than 80°C. Etch patterns with better-defined side faces are formed by anisotropic etching with the addition of hydrogen peroxide.

Equations of ideal magnetohydrodynamics that describe stationary flows of an inviscid ideally electrically conducting fluid are considered. Classes of exact solutions of these equations are described. With the use of the natural curvilinear coordinate system, where the streamlines and magnetic force lines play the role of the coordinate curves, the model equations are partially integrated and converted to the form that is more convenient for the description of the magnetic lines and streamlines of particles. As the coordinate system used is related to the initial coordinate system by a nonlocal transformation, the group admitted by the system can change. An infinite-dimensional (containing three arbitrary functions of time) group of symmetries is calculated for the system in the natural coordinates. An optimal system of subgroups of dimensions 1 and 2 is constructed for this group. For one of the optimal system subgroups, an invariant exact solution is found, which describes the electrically conducting fluid flow of the vortex source type with swirling magnetic lines and streamlines.

The paper discusses the types and methods of control measures and their implementation by individual authorities at the federal and regional levels, as part of the implementation of the National Healthcare project. This study aims to develop measures to control the implementation of the National Project at all stages. The features of monitoring the implementation of the National Project in the Electronic Budget system are examined. The requirements established by regulatory legal acts to assess the effectiveness and efficiency of using inter-budget transfers are analyzed. Based on the study results, the authors formulated proposals for the implementation of preliminary, current, and subsequent financial control. It is concluded that it is necessary to conduct field monitoring activities to check for compliance with the data entered in the Electronic Budget system and strengthen the direction of preventive component.

In our previous works (Baykin and Golovin 2016, 2017) it is shown that inhomogeneity of the permeability of a reservoir might play a significant role in the choice of the direction of the hydraulic fracture propagation. This effect was demonstrated using the fully coupled model of the hydraulic fracture in the poroelastic medium under the restriction on the geometry of the fracture similar to the one used in the Khristianovich–Geertsma–de Klerk model. In present paper, we extend our observations to a model of the planar 3D hydraulic fracture in the inhomogeneous poroelastic medium. In a series of numerical experiments we demonstrate that, depending on the permeability contrast of different parts of a layered reservoir, the hydraulic fracture propagates either within the low-permeable or the high-permeable zones of the reservoir. This behaviour is explained by the non-uniform action of the backstress that is formed on the fracture walls due to the pressure of the pore fluid.

In this paper we demonstrate the influence of the pore pressure on the development of a hydraulically-driven fracture in a poroelastic medium. We present a novel numerical model for propagation of a planar hydraulic fracture and prove its correctness by the analysis of the numerical convergence and by the comparison with known solutions. The advantage of the algorithm is that it does not require distinguishing of the fracture's tips and reconstruction of the numerical mesh according to the fracture propagation. Next, we perform a thorough analysis of the interplay of fluid filtration and redistribution of stresses near the fracture. We demonstrate that the fracture length decreases with the increase of the Biot's number (the parameter that determines the contribution of the pore pressure to the stress) and explain this effect by analysing the near-fracture pore pressure, rock deformation and stresses. We conclude that the correct account for the fluid exchange between the fracture and the rock should be based not only on physical parameters of the rock and fluid, but also on the analysis of stresses near the fracture.

A system is described for development of new products and technology based on modeling, simulation, and laboratory testing for processes applied to VMZ 5000 rolling mill conditions. Approaches are demonstrated for creating slab heating technology using mathematical modeling of carbonitride particle dissolution and austenite grain growth as well as an approach to creating strategies for rough rolling by new Hot Rolling Recrystallization Model (HRRM) software and the finishing stage. Specific features of rolled product structure formation during cooling and alloying concepts in relation to steel strength class are described. Results are given for industrial production, including steels for underwater pipelines and pipelines in areas near active tectonic faults.

A comparative study is provided for the effect of different alloying versions on phase transformation, structure, and mechanical properties of low-alloy pipe steel. Steel alloyed economically with chromium is developed for producing sheet 21.6 (21.7) and 25.8 mm thick of strength class K60 intended for manufacturing pipe up to 1420 mm in diameter for main pipelines with a working pressure of up to 9.8 MPa.

A one-dimensional model is proposed for transportation of a two-phase fluid (sandcontaining fluid and pure fluid) in the Hele-Shaw cell with permeable walls through which the pure fluid can leak off, causing the growth of the sand concentration. The model describes the process of pure fluid displacement with the emergence of the Saffman–Taylor instability and extends Koval’s model to the case of sand concentration variation owing to pure fluid outflow through the cell walls. The Riemann problem is analyzed. New flow configurations, which are not predicted by Koval’s model, are discovered.

Kinetics of austenite phase transformation in previously deformed steels of different alloy systems during continuous cooling are studied. It is shown that with a basic chemical composition of 0.06% C and 1.55% Mn–Nb–Ti alloying with chromium (0.19%) leads to the formation after cooling of an almost identical microstructure, as also with addition of molybdenum (0.14%), from the point of view of fineness and hardness. An optimum steel alloy system is suggested from an economic point of view that provides the required set of properties for rolled sheet more than 30 mm thick of strength category X65 produced under conditions of the VMZ (Vyksa) sheet rolling complex (5000 mill).

The paper presents a model of a cerebral vascular system including two types of vessel networks (arterial and venous) joined by a porous medium as a substitute to a microcapillary system. The aim of the paper is to reproduce numerically experimental data on endovascular measurements of fluid velocity and pressure in the afferent artery and the efferent vein of the arteriovenous malformation (AVM). The suggested model qualitatively simulates all the main features of the experimental $vp$-diagrams: presence of the time shift between velocity and pressure waves, semicircular shape of the diagram, difference in the direction of circulation in the arterial and venous parts and upper-left drift of the diagram during the embolisation of the AVM. The velocity–pressure time shift is analysed on the modelling example of pulsation flow within a vessel in a cylindrical porous medium. The demonstrated adequacy of the model allows its further use for simulation of various strategies of AVM treatment, haemorrhage risk estimations, etc.

This paper presents the coupled model of a hydraulic fracturing and proppant transport. The former is described in terms of enhanced pseudo-3D model that considers height growth across two symmetric stress barriers, while the latter is given by two-dimensional transport model, stemming from the solution of an elliptical equation for fluid pressure and advection equation for the proppant transport. These two sub-modules are solved numerically using implicit time integration in hydraulic part and explicit time stepping in the transport part. In addition to that, interpolation is used to couple the two models with different grids. Results of several numerical simulations are presented for different configurations to demonstrate the interplay between these two modules. In particular, the developed coupled scheme allows us to study phenomena associated with complex fluid flow within the fracture, such as for the case of Saffman-Taylor instability., Although the EP3D model was used in this study, the Planar3D model is a benchmark for engineering simulators that are currently being developed. Authors have understood how to represent the better agreement between results by both models, how to explain results in coupled model in more general sense, so we need to withdraw the manuscript and re-submit it in significantly updated form

This paper presents an analytic self-similar solution describing an equilibrium of a planar semi-infinite hydraulic fracture in a poroelastic medium. The equilibrium of the fracture is sustained by a balance between the pressure of fluid within the fracture and the confining stress due to elasticity of nearby poroelastic material satisfying the Biot model assumptions. Propagation of fluid in the fracture, leakoff through the fracture’s walls and filtration in the poroelastic medium towards the fracture’s tip form a dipole-type pattern of flow. The solution is used for the verification of a numerical algorithm developed earlier for the pressure transient analysis in water injection wells.

The paper addresses the problem of modeling a fracture propagation in linear elastic porous media driven by injection of non-Newtonian power-law fluid. The model involves the lubrication theory equation expressing the mass conservation of fluid and a nonlocal singular integral relation for the fracture aperture as a functional of the fluid pressure. We assume only the viscosity-dominated case in which the fracture toughness is neglected. This allows considering the fracture as an opened part of a preexisting closed fracture of larger length. The numerical method consists in solving equations of the model over the whole length of the preexisting fracture without distinguishing the tip region of the opened part. The problem is solved via the finite element method. The weak formulation of the solution allows pressure singularity with the required asymptotics near the fracture tip. Comparison of the numerical and the exact self-similar solutions in the case of a constant flow rate, zero fluid leakoff, and zero fracture toughness reveals the accuracy of the approximate solution to at least O(h1/2), where h is the maximal linear size of the grid cells. As an illustration, we also demonstrate the numerical experiments with periodic fluid injection and variable fluid efficiency.

In this paper we study the pressure drop in a hydraulic fracture after shut-in of a water injection well. The pressure transient behavior depends on fracture closure, lateral stress, rock elasticity and fracture fluid leak-off. Under the assumption that horizontal cross-sections of a vertical fracture do not depend on the vertical variable, we formulate a mathematical model which allows for determination of both pore pressure and elastic rock displacements jointly with the fracture aperture and fracture fluid pressure. An analytical consideration is performed for the case of an ideal very long fracture with the same aperture along its full length. In the general case, fracture closure is analyzed numerically.

Production of plates of strength category DNV SAWL 450 SFDU, intended for manufacturing pipe with a 39 mm wall thickness for submarine pipelines, is mastered under industrial conditions at the 5000 mill of Vyksa Metallurgical Plant (VMZ). The effect of chemical composition and steel manufacturing technology on features of microstructure formation (including its morphological features and excess phase precipitation) is studied. This makes it possible to formulate the optimum ferrite-bainite microstructure after TMT and provide the required strength level and cold resistance for plates, including manufacture of double length workpieces.

Exact solutions of the equations of ideal magnetohydrodynamics describing the class of unsteady flows of an electrically conducting fluid with a constant total pressure are constructed. The solutions are written in the Lagrange coordinate system; arbitrariness in its choice was used to parameterize magnetic field lines. The wide functional arbitrariness the solutions provide a significant variation in the picture of the described fluid motions. An example of unsteady flow of an ideal electrically conducting fluid in a cylindrical channel with fixed magnetic tubes is given.

The paper is devoted to comparison of multiple-objectives optimization algorithms in application to the problem of design optimization of a multiply fractured horizontal well (MFHW). The problem is stated either as a single-objective one, where only the income based on Net Present Value (NPV) is maximized, or as a multi-objective problem, where it is necessary to simultaneously find extremes of NPV, the post-fracture oil production and fracturing costs. Three popular stochastic optimization methods are considered: genetic algorithms (GA), simulated annealing (SA) and particle swarm optimization (PSO). Since PSO, SA and GA techniques employ different strategies and computational efforts, the comparison of their efficiency was carried out by testing on synthetic problems and then applied to the example of a MFHW in a low-permeable oil reservoir.

An exact solution of the magnetohydrodynamic equations is constructed which describes steady vortex flow in a stationary cylinder on the axis of which a conductor carrying a known current is located. The solution is obtained under the assumption that the fluid is viscous and has finite electrical conductivity and that the magnetic field has only the axial and azimuthal components in a cylindrical coordinate system. It is found that the action of the Lorentz force is compensated by changing the pressure. Fluid flow occurs from the periphery to the axis of the cylinder under a pressure gradient, with flow rotation and swirling. The fluid flow causes a concentration of the magnetic lines near the axis of the cylinder, providing an exponential decrease in the magnetic field strength with distance from the axis. This flow can be considered as a model of a local increase in the magnetic field strength due to the transfer of its force lines by the flow of the electrically conducting fluid.

D M Markovich and S V GolovinThe origins of the Conference start from 1970 in the Soviet Union, Novosibirsk. It was organized by Kutateladze Institute of Thermophysics SB RAS. The name of the conference was «Actual problems of thermophysics and physical hydrodynamics». The conference has been organized under this name up to 2015. The conference chairs were academicians V.E. Nakoryakov, S. V. Alekseenko and corresponding member of RAS D. M. Marckovich. Peer reviewed proceedings of the conference have been published in the format of printed books. In 2016 the conference is reorganized in a new format with a shorter name: «Thermophysics and physical hydrodynamics».The conference takes place in Yalta, a beautiful city in Crimea on the bank of the Black Sea. Lavrentev Institute of hydrodynamics and the National committee on heat and mass transfer are among other conference organizers besides Kutateladze Institute of thermophysics. The present Conference covers the following topics: heat transfer and hydrodynamics in single phase flows, hydrodynamics and heat and mass transfer in multiphase flows, phase transitions, reacting flow dynamics, detonation processes, numerical methods in thermophysics and physical hydrodynamics, techniques of thermophysics and hydrodynamics experiment, thermophysical properties of substances and new materials, heat transfer and hydrodynamics on micro- and nanoscales, electrophysical phenomena in gaseous and liquid media, heat transfer and hydrodynamics in industrial processes and environment protection.There are more than 200 participants. The proceedings contain 156 papers grouped by topic. The scientific committee appreciates the enormous work of the editorial board and reviewers in the preparation of this volume. We would like to express our sincere thanks to all authors for their research contributions, and also to organizers of the conference for their valuable spadework.List of Photos and Sponsor acknowledgements are available in this PDF

The approach to the problem of hydraulic fracturing design optimization is proposed which combines three modules: a fracture geometry module, an oil production module and an economic module. The approach is based on the genetic algorithm — the universal multivariate and multiobjective optimization method. The optimization process involves subsequent determination of the fracture geometry, calculation of the oil production depending on the number of fractures, and description of the investment–return cash flows. Iterated by the genetic algorithm for different set of input parameters, this approach allows determination of the optimal design of a multiply fractured well for a given set of geological and economical information. The results show that the proposed method is plausible and can be useful for achieving projected objectives.

Incompressible stationary flows of ideal plasma are studied. By introduction of curvilinear system of coordinates in which streamlines and magnetic force lines form a family of coordinate surfaces, MHD equations are partially integrated and brought to a certain convenient form. It is demonstrated that the admissible group of Bogoyavlenskij's symmetry transformations (Bogoyavlenskij, 2001 [1] ) performs as a scaling transformation (the scaling factor is an arbitrary function of one variable) for the curvilinear coordinates. Analytic description of stationary flows with constant total pressure is given. It is shown, that contact magnetic surfaces of such flows are translational surfaces, i.e. are swept out by translating one curve rigidly along another curve. Examples of solutions with constant total pressure possessing an arbitrariness in one function of two variables and three functions of one variable are given.

All irreducible regular partially invariant submodels with one noninvariant function for the equations of ideal magnetohydrodynamics are constructed. The submodels are completed to involution, and partially integrated. The submodels specify Ovsyannikov vortex type motion or motion with homogeneous deformation in some spatial directions.

The physical properties of ideal plasma flow described by the Ovsyannikov plane vortex are studied. The particle trajectories and magnetic lines are shown to be plane curves, and an algorithm for describing the motion in three-dimensional space is proposed. Some exact solutions of the submodel are obtained and studied.

A submodel of the equations of ideal magnetohydrodynamics is constructed that generalizes the classical motion of an ideal continuous medium with plane waves. It is shown that, in contrast to classical motion, in this submodel the velocity and magnetic-field vectors can change direction in a plane orthogonal to a distinguished spatial direction. The submodel is described by a system of equations with two independent variables and a finite relation specifying the orientation of the vector fields in space. The solutions of the submodel define substantially spatial processes and singularities in the motion of continuous media which cannot be studied in the classical one-dimensional formulation.

A geometrical description of three-dimensional irrotational vector fields which are partially invariant with respect to the SO(3) group of rotations is given. It is shown that the motion of a continuum, that satisfies the equation of continuity and is partially invariant with respect to SO(3), is necessarily rotational, that is, the curl of the velocity vector is non zero.

A continuous demand for thick plates for structural applications with yield strength of 450–485 MPa, high toughness and cold resistance requires the development of new methods of additional grain refinement at all stages of thermo-mechanical control process (TMCP). The effect of Ti-Nb precipitates morphology on grain growth during reheating was investigated. It has been shown that Nb is a key element for grain growth control. Submicron Nb carbonitrides suppress austenite grain growth at lower slab reheating temperatures. The effect of Ti additions on suppression of grain growth during low-temperature reheating is negligible. Parameters of reheating such as duration and temperature were adjusted in order to maximize the effect of Nb microalloying and to receive finer austenite grain before hot rolling. Grain refinement in the course of hot deformation was studied through physical modeling. Using the recrystallization model, new rolling schedules were introduced. Industrial trials were conducted; the effect of reheating and deformation parameters on cold resistance of steel was investigated. Implementation of the results of given study into production practice made it possible to produce plates with excellent set of properties, including strength, toughness, and cold resistance.

Specialists at the company Severstal’ and the Central Research Institute of Ferrous Metallurgy have developed a chemical composition and technology for making steel of strength class X56, and they have also produced a commercial batch of this steel. Production of the batch on the 5000 mill at Severstal’ entailed the use of a modern controlled-rolling technology together with accelerated cooling, which made it possible to obtain the required set of characteristics in thick plates. The Vyksa Metallurgical Plant converted the plates into 762-mm-diam. conductor pipe with a wall thickness of 38.1 mm. Analysis of the effect of the tube conversion on the mechanical characteristics of the steel showed that the changes which take place in the mechanical characteristics of the base metal during the formation of thick-walled tubes must be taken into account when specifications are developed for the flat-rolled products used to make these tubes.

We give a description of the ideal plasma flow, which is governed by an exact partially invariant solution of the magnetohydrodynamics equations. The solution generalizes known one-dimensional flow with spherical waves. The generalization consists in addition of the special tangent vector components of the velocity and the magnetic field at any plasma particle. In the special case of zeroth tangential component the solution coincides with the classical one-dimensional one. This paper describes a three-dimensional picture of the plasma flow, governed by the obtained solution.

We investigate properties of plasma flow, governed by an exact reduction of the ideal magnetohydrodynamics equations which was obtained in our recent article. The reduction is called a singular vortex. It gives a description of a three-dimensional nonstationary plasma flow in terms of solution of reduced system of PDEs with two independent variables. In this paper we investigate symmetry properties of the reduced system and construct its invariant solutions. Also we give a description of the physical features of plasma motion, governed by the singular vortex. Namely, we prove that in the observed class of solutions the particles trajectories as well as magnetic field lines are flat curves. The position and orientation of the plane containing the particle's trajectory depends on the initial position of the particle. We describe the shape of trajectories and magnetic field lines for the cases of stationary and self-similar plasma flow.

We obtain an exact solution of the ideal magnetohydrodynamics equations in (3+1) dimensions. The construction of the solution is based on the invariants of the group O(3) of rotations. It is a deep generalization of the known solution, which describes a radial flow with spherical waves. It is shown that in the irreducible solution, the velocity and magnetic field vectors of the particle are coplanar to the radius vector of the particle. The solution is represented as an involutive invariant subsystem of PDEs with two independent variables and finite relation, which contains a functional arbitrariness.

A full description of irrotational ideal gas motions is given, in which pressure depends only on time. It is shown that under such motions the dependence of velocity vector on spatial coordinates is linear and of a special kind.

An exact solution is constructed, which describes a gas glow in a strip between a rectilinear source and sink. With time, the strip turns and expands. In the case of consistent boundary conditions, the flow in the strip is continuous. If the consistency constraints are violated, a shock wave is formed inside the strip.

The bases of differential invariants for infinite-dimensional Lie groups, admitted by the Navier–Stokes and gas dynamics equations, are calculated. The possibilities of bases application to construct differentially invariant solutions are shown. In the terms of differential invariants the group interpretations of Karman’s solution, describing a liquid flow between rotating disks, and solution, giving a stationary cylindrical vortex in a viscous fluid, are given. The application of the bases of differential invariants to construct the group stratification of equations is shown by two examples. The examples are the group stratification for the stationary gas dynamics and for the transonic gas motion equations. The possibilities of group stratification use to form new group-invariant solutions are analyzed.

Exact solutions of the Karman–Guderley equation that describes spatial gas flows in the transonic approximation are considered. A group stratification of the equation with respect to the infinite-dimensional part of the admissible group is constructed. New invariant and partly invariant solutions are obtained. The possibility of existence of solutions continuous in the entire space is analyzed for invariant submodels with one independent variable. A solution of the Karman–Guderley equation of the double-wave type is constructed.