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In this paper, we study the observability and controllability of wave equations coupled by first or zero order terms on a compact manifold. We adopt the approach in Dehman-Lebeau's paper [B. Dehman and G. Lebeau, SIAM J. Control Optim.48 (2009) 521–550.] to prove that: the weak observability inequality holds for wave equations coupled by first order terms on compact manifold without boundary if and only if a class of ordinary differential equations related to the symbol of the first order terms along the Hamiltonian flow are exactly controllable. We also compute the higher order part of the observability constant and the observation time. By duality, we obtain the controllability of the dual control system in a finite co-dimensional space. This gives the full controllability under the assumption of unique continuation of eigenfunctions. Moreover, these results can be applied to the systems of wave equations coupled by zero order terms of cascade structure after an appropriate change of unknowns and spaces. Finally, we provide some concrete examples as applications where the unique continuation property indeed holds. [ABSTRACT FROM AUTHOR]

The Sterile Insect Technique (SIT) is a classic vector control method that has been successfully applied to fight against diverse insect plagues since the 1950s. In recent years, this strategy has been used to control mosquito populations, in order to limit the spread of the diseases they transmit. In this paper, we consider a system of reaction-diffusion equations to model the mosquito population and study the effect of the release of sterile mosquito males. Then, we propose to analyze the release in a limited area inside a wider area containing a natural mosquito population. We are interested in protecting a mosquito free region from invasion by mosquitoes from an exterior domain by controlling the population in a release band at the border between the two regions: we construct a barrier blocking the invasion of mosquitoes from the exterior. We adapt the geometric method of Lewis and Keener (see Lewis and Keener [SIAM J. Appl. Math.61 (2000) 293-316]) in this framework and extend their main result to find relations on the size of the release region and the density of the released sterile males that allow us to block the invasion. Numerical simulations are also performed to illustrate our results. [ABSTRACT FROM AUTHOR]

The paper analyzes the Morley element method for the Cahn–Hilliard equation. The objective is to prove the numerical interfaces of the Morley element method approximate the Hele-Shaw flow. It is achieved by establishing the optimal error estimates which depend on 1/ε 1 ε $ \frac{1}{\epsilon }$ polynomially, and the error estimates should be established from lower norms to higher norms progressively. If the higher norm error bound is derived by choosing test function directly, we cannot obtain the optimal error order, and we cannot establish the error bound which depends on 1/ε 1 ε $ \frac{1}{\epsilon }$ polynomially either. Different from the discontinuous Galerkin (DG) space [Feng et al. SIAM J. Numer. Anal.54 (2016) 825–847], the Morley element space does not contain the finite element space as a subspace such that the projection theory does not work. The enriching theory is used in this paper to overcome this difficulty, and some nonstandard techniques are combined in the process such as the a priori estimates of the exact solution u, integration by parts in space, summation by parts in time, and special properties of the Morley elements. If one of these techniques is lacked, either we can only obtain the sub-optimal piecewise L∞(H2) error order, or we can merely obtain the error bounds which are exponentially dependent on 1/ε 1 ε $ \frac{1}{\epsilon }$. Numerical results are presented to validate the optimal L∞(H2) error order and the asymptotic behavior of the solutions of the Cahn–Hilliard equation. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyze a fully discrete finite element projection method for the magnetohydrodynamic (MHD) equations. A modified Crank–Nicolson method and the Galerkin finite element method are used to discretize the model in time and space, respectively, and appropriate semi-implicit treatments are applied to the fluid convection term and two coupling terms. These semi-implicit approximations result in a linear system with variable coefficients for which the unique solvability can be proved theoretically. In addition, we use a second-order decoupling projection method of the Van Kan type [Van Kan, SIAM J. Sci. Statist. Comput.7 (1986) 870–891] in the Stokes solver, which computes the intermediate velocity field based on the gradient of the pressure from the previous time level, and enforces the incompressibility constraint via the Helmholtz decomposition of the intermediate velocity field. The energy stability of the scheme is theoretically proved, in which the decoupled Stokes solver needs to be analyzed in details. Error estimates are proved in the discrete L∞(0, T; L2) norm for the proposed decoupled finite element projection scheme. Numerical examples are provided to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

The popular (piecewise) quadratic schemes for the biharmonic equation based on triangles are the nonconforming Morley finite element, the discontinuous Galerkin, the C0 interior penalty, and the WOPSIP schemes. Those methods are modified in their right-hand side F ∈ H−2(Ω) replaced by F ○ (JIM) and then are quasi-optimal in their respective discrete norms. The smoother JIM is defined for a piecewise smooth input function by a (generalized) Morley interpolation IM followed by a companion operator J. An abstract framework for the error analysis in the energy, weaker and piecewise Sobolev norms for the schemes is outlined and applied to the biharmonic equation. Three errors are also equivalent in some particular discrete norm from [Carstensen, Gallistl, Nataraj, ESAIM: M2AN49 (2015) 977–990.] without data oscillations. This paper extends the work [Veeser and Zanotti, SIAM J. Numer. Anal.56 (2018) 1621–1642] to the discontinuous Galerkin scheme and adds error estimates in weaker and piecewise Sobolev norms. [ABSTRACT FROM AUTHOR]

In this paper, we propose and study the uniaxial perfectly matched layer (PML) method for three-dimensional time-domain electromagnetic scattering problems, which has a great advantage over the spherical one in dealing with problems involving anisotropic scatterers. The truncated uniaxial PML problem is proved to be well-posed and stable, based on the Laplace transform technique and the energy method. Moreover, the L2-norm and L∞-norm error estimates in time are given between the solutions of the original scattering problem and the truncated PML problem, leading to the exponential convergence of the time-domain uniaxial PML method in terms of the thickness and absorbing parameters of the PML layer. The proof depends on the error analysis between the EtM operators for the original scattering problem and the truncated PML problem, which is different from our previous work (Wei et al. [SIAM J. Numer. Anal.58 (2020) 1918–1940]). [ABSTRACT FROM AUTHOR]

By combining a certain approximation property in the spatial domain, and weighted 𝓁2-summability of the Hermite polynomial expansion coefficients in the parametric domain obtained in Bachmayr et al. [ESAIM: M2AN51 (2017) 341–363] and Bachmayr et al. [SIAM J. Numer. Anal.55 (2017) 2151–2186], we investigate linear non-adaptive methods of fully discrete polynomial interpolation approximation as well as fully discrete weighted quadrature methods of integration for parametric and stochastic elliptic PDEs with lognormal inputs. We construct such methods and prove convergence rates of the approximations by them. The linear non-adaptive methods of fully discrete polynomial interpolation approximation are sparse-grid collocation methods which are certain sums taken over finite nested Smolyak-type indices sets of mixed tensor products of dyadic scale successive differences of spatial approximations of particular solvers, and of successive differences of their parametric Lagrange interpolating polynomials. The Smolyak-type sparse interpolation grids in the parametric domain are constructed from the roots of Hermite polynomials or their improved modifications. Moreover, they generate in a natural way fully discrete weighted quadrature formulas for integration of the solution to parametric and stochastic elliptic PDEs and its linear functionals, and the error of the corresponding integration can be estimated via the error in the Bochner space L1 (ℝ∞, V, γ) norm of the generating methods where γ is the Gaussian probability measure on ℝ∞ and V is the energy space. We also briefly consider similar problems for parametric and stochastic elliptic PDEs with affine inputs, and problems of non-fully discrete polynomial interpolation approximation and integration. In particular, the convergence rates of non-fully discrete polynomial interpolation approximation and integration obtained in this paper significantly improve the known ones. [ABSTRACT FROM AUTHOR]

In this paper, we study the central discontinuous Galerkin (DG) method on overlapping meshes for second order wave equations. We consider the first order hyperbolic system, which is equivalent to the second order scalar equation, and construct the corresponding central DG scheme. We then provide the stability analysis and the optimal error estimates for the proposed central DG scheme for one- and multi-dimensional cases with piecewise Pk elements. The optimal error estimates are valid for uniform Cartesian meshes and polynomials of arbitrary degree k ≥ 0. In particular, we adopt the techniques in Liu et al. (SIAM J. Numer. Anal.56 (2018) 520–541; ESAIM: M2AN54 (2020) 705–726) and obtain the local projection that is crucial in deriving the optimal order of convergence. The construction of the projection here is more challenging since the unknowns are highly coupled in the proposed scheme. Dispersion analysis is performed on the proposed scheme for one dimensional problems, indicating that the numerical solution with P1 elements reaches its minimum with a suitable parameter in the dissipation term. Several numerical examples including accuracy tests and long time simulation are presented to validate the theoretical results. [ABSTRACT FROM AUTHOR]

Copyright of Natures Sciences Sociétés is the property of EDP Sciences and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Parasite (1252607X) is the property of EDP Sciences and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We verify strong rates of convergence for a time-implicit, finite-element based space-time discretization of the backward stochastic heat equation, and the forward-backward stochastic heat equation from stochastic optimal control. The fully discrete version of the forward-backward stochastic heat equation is then used within a gradient descent algorithm to approximately solve the linear-quadratic control problem for the stochastic heat equation driven by additive noise. This work is thus giving a theoretical foundation for the computational findings in Dunst and Prohl, SIAM J. Sci. Comput.38 (2016) A2725–A2755. [ABSTRACT FROM AUTHOR]

Within the framework of viscosity solution, we study the relationship between the maximum principle (MP) from M. Hu, S. Ji and X. Xue [SIAM J. Control Optim.56 (2018) 4309–4335] and the dynamic programming principle (DPP) from M. Hu, S. Ji and X. Xue [SIAM J. Control Optim.57 (2019) 3911–3938] for a fully coupled forward–backward stochastic controlled system (FBSCS) with a nonconvex control domain. For a fully coupled FBSCS, both the corresponding MP and the corresponding Hamilton–Jacobi–Bellman (HJB) equation combine an algebra equation respectively. With the help of a new decoupling technique, we obtain the desirable estimates for the fully coupled forward–backward variational equations and establish the relationship. Furthermore, for the smooth case, we discover the connection between the derivatives of the solution to the algebra equation and some terms in the first-order and second-order adjoint equations. Finally, we study the local case under the monotonicity conditions as from J. Li and Q. Wei [SIAM J. Control Optim.52 (2014) 1622–1662] and Z. Wu [Syst. Sci. Math. Sci.11 (1998) 249–259], and obtain the relationship between the MP from Z. Wu [Syst. Sci. Math. Sci.11 (1998) 249–259] and the DPP from J. Li and Q. Wei [SIAM J. Control Optim.52 (2014) 1622–1662]. [ABSTRACT FROM AUTHOR]

We study the strong stabilization of wave equations on some sphere-like manifolds, with rough damping terms which do not satisfy the geometric control condition posed by Rauch-Taylor [J. Rauch and M. Taylor, Commun. Pure Appl. Math. 28 (1975) 501-523] and Bardos-Lebeau-Rauch [C. Bardos, G. Lebeau and J. Rauch, SIAM J. Control Optimiz. 30 (1992) 1024-1065]. We begin with an unpublished result of G. Lebeau, which states that on Sd, the indicator function of the upper hemisphere strongly stabilizes the damped wave equation, even though the equators, which are geodesics contained in the boundary of the upper hemisphere, do not enter the damping region. Then we extend this result on dimension 2, to Zoll surfaces of revolution, whose geometry is similar to that of S². In particular, geometric objects such as the equator, and the hemi-surfaces are well defined. Our result states that the indicator function of the upper hemi-surface strongly stabilizes the damped wave equation, even though the equator, as a geodesic, does not enter the upper hemi-surface either. [ABSTRACT FROM AUTHOR]

The article presents the study which investigated the prevalence of the opportunistic intestinal pathogen Enterocytozoon (E.)bieneusi among children in rural communities in Western and Northern Thailand. In the study, three genotypes of the pathogen were identified, namely, genotype D predominated, EbpC, and the novel genotype ETMK1. The methods used in the study are nested polymerase chain reaction (PCR), genotype characterization, and host specificity.

The fish and invertebrate behavior of the Ubol Ratana Reservoir, Thailand, were monitored using up- and downlooking split beam sonar located at a fixed location. In the same area and period, ichthyoplankton nets and multimesh gillnets were used. The bulk of targets, recorded by acoustics and direct capture, consisted both of fish 3–4 cm long and insect larvae 0.2–1 cm long. Diurnal patterns of behavior were very distinct: during the daytime, invertebrates were hidden in the bottom and most fish stayed in compact shoals. Time course of acoustic fish biomass and abundance was very variable due to shoaling. Only the largest fish were recorded as solitary targets. At night, the whole acoustic range was filled with targets and the time course of fish biomass (5–15 kg ha–1) and abundance (20–45 thousand individuals ha–1) were more constant. The biomass increased mostly at surface layers. Fish appeared in the evening in the water column 1 h earlier and stayed there in the morning 1 h longer than invertebrates. Dawn and dusk are good periods for studying fish before invertebrates outnumber them. Apart from fish, according to the target strength, swimming speed and depth distribution, at least four groups of water invertebrates were distinguished acoustically, some with extremely fast vertical movement (7–9 cm s–1 vertical speed). Comparison of up- and downlooking observations gave comparable results in midwater layer outside the near-field of the transducer. The uplooking approach can be more suitable for night records; downlooking for the day. [Copyright &y& Elsevier]