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In this paper, we are interested in some theoretical and numerical studies of a special case of a degenerate nonlinear Schrödinger equation namely the so-called Gross-Pitaevskii Equation(GPE). More precisely, we will treat in a first time the well-posedness of GPE model with a degeneracy occurring in the interior of the space variable domain, i.e ∃x0 ∈ (0, L), s. t k(x0) = 0, where k stands for the diffusion coefficient and L is a positive constant. Thereafter, we will focus ourselves on some numerical simulations showing the influence of a different parameters, especially the interior degeneracy, on the behavior of the wave solution corresponding to our model in a special case of the function k namely k(x) = |x − x0| α, α ∈ (0, 1).

In this paper, we consider a coupled system of two biharmonic equations with damping and source terms of variable-exponent nonlinearities, supplemented with initial and mixed boundary conditions. We establish an existence and uniqueness result of a weak solution, under suitable assumptions on the variable exponents. Then, we show that solutions with negative-initial energy blow up in finite time. To illustrate our theoritical findings, we present two numerical examples. [ABSTRACT FROM AUTHOR]

In this work we study the well-posedness and the asymptotic stability of a linear thermoelastic Timoshenko system free of second spectrum, where the heat conduction is given by Cattaneo's law. We give a detailed proof of the well-posedness, using the semigroup theory. Then, we prove that the system is exponentially stable irrespective of the coefficients. We also illustrate our theoretical results by performing some numerical tests. [ABSTRACT FROM AUTHOR]

In this paper, we present a numerical approach to an inverse problem of a population dynamics model. We propose a numerical approximation of the optimal control for obtaining the desired observation state using the augmented Lagrangian method. Moreover, the existence and uniqueness of the numerical solutions are mathematically investigated in this work. Finally, we present some numerical experiments to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we consider a one-dimensional linear Bresse system with only one infinite memory term acting in the third equation (longitudinal displacements). Under a general condition on the memory kernel (relaxation function), we establish a decay estimate of the energy of the system. Our decay result extends and improves some decay rates obtained in the literature such as the one in [27], [4], [33], [58] and [34]. The proof is based on the energy method together with convexity arguments. Numerical simulations are given to illustrate the theoretical decay result. [ABSTRACT FROM AUTHOR]

In this paper, we consider a memory-type swelling porous-elastic system. First, we use the multiplier method to prove explicit and general decay results to solutions of the system with sufficient regularities. These decay results are established under a very general assumption on the relaxation function and for suitable given data. We also perform several numerical tests to illustrate our theoretical decay results. Our results generalize and improve many earlier results in the literature. [ABSTRACT FROM AUTHOR]

Problems with variable exponents have attracted a great deal of attention lately and various existence, nonexistence and stability results have been established. The importance of such problems has manifested due to the recent advancement of science and technology and to the wide application in areas such as electrorheological fluids (smart fluids) which have the property that the viscosity changes drastically when exposed to heat or electrical fields. To tackle and understand these models, new sophisticated mathematical functional spaces have been introduced, such as the Lebesgue and Sobolev spaces with variable exponents. In this work, we are concerned with a system of wave equations with variable-exponent nonlinearities. This system can be regarded as a model for interaction between two fields describing the motion of two "smart" materials. We, first, establish the existence of global solutions then show that solutions of enough regularities stabilize to the rest state (0 , 0) either exponentially or polynomially depending on the range of the variable exponents. We also present some numerical tests to illustrate our theoretical findings. [ABSTRACT FROM AUTHOR]

In this work, we consider a swelling porous-elastic system coupled with a heat system of second sound. We establish the existence of solutions then we prove an exponential decay result. Unlike the "purely" porous system, this result is obtained without the equal-speed requirement. We also perform some numerical tests to illustrate our theoretical findings. [ABSTRACT FROM AUTHOR]

In this paper, we present a fast algorithm of the nonparametric elastic image registration using a simple implementation of the Range Restricted GMRES (RRGMRES) method. This approach differs from the others in the fact that it is specified to the tridiagonal block matrix type to resolve a nonsymmetric linear system. In what follows, we prove existence and uniqueness of minimizer of the elastic registration problem and present the corresponding discrete problem by employing a finite difference scheme. The accuracy of the proposed method is demonstrated on different image registration examples; we also show the speedup of the proposed approach by calculating the corresponding CPU time and compared it with the classical elastic registration method. [ABSTRACT FROM AUTHOR]

Here, the authors propose a spatially weighted super‐resolution (SR) algorithm, which takes into consideration the distribution of every information that characterise different image areas. The authors investigate to use a combined spatially weighted regularisation of the bilateral total variation and a second‐order term increasing then the robustness of the proposed SR approach with respect to blur and noise degradations. In addition, the authors propose an iterative Bregman iteration algorithm to resolve the obtained optimisation SR problem. As a result, this regularisation is more efficient and easier to implement; moreover, it preserves well the smooth regions of the image and also sharp edges. Using different simulated and real tests, the authors prove the efficiency of the proposed algorithm compared to some SR methods. [ABSTRACT FROM AUTHOR]

In this work, a type III thermo‐porous elastic system is considered. First, we use the semigroup theory to demonstrate that the system is well‐posed. Second, we show that the system is exponentially stable under a natural constraint on its parameters. Finally, we provide various numerical examples to illustrate numerically our theoretical findings. [ABSTRACT FROM AUTHOR]

In this article, we consider a coupled system of two nonlinear hyperbolic equations, where the exponents in the damping and source terms are variables. First, we prove a theorem of existence and uniqueness of weak solution, by using the Faedo Galerkin approximations and the Banach fixed point theorem. Then, using the energy method, we show that certain solutions with positive initial energy blow up in finite time. We also give some numerical applications to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]