An adaptive numerical method for the wave equation with a nonlinear boundary condition.
An age-dependent model describing the spread of panleucopenia virus within feline populations
Global existence results and long time behavior are provided for a mathematical model describing the propagation of Feline Panleucopenia Virus (FPLV) within a domestic cat population; two transmission modes are involved: a direct one from infective cats to susceptible ones, and an indirect one from the contaminated environment to susceptible cats. A more severe impact of the virus on young cats requires an age-structured model.
An almost-everywhere solution to a mixed problem for one degenerate linear evolution system.
An analysis of the influence of data extrema on some first and second order central approximations of hyperbolic conservation laws
We discuss the occurrence of oscillations when using central schemes of the Lax-Friedrichs type (LFt), Rusanov’s method and the staggered and non-staggered second order Nessyahu-Tadmor (NT) schemes. Although these schemes are monotone or TVD, respectively, oscillations may be introduced at local data extrema. The dependence of oscillatory properties on the numerical viscosity coefficient is investigated rigorously for the LFt schemes, illuminating also the properties of Rusanov’s method. It turns...
An analysis of the influence of data extrema on some first and second order central approximations of hyperbolic conservation laws
We discuss the occurrence of oscillations when using central schemes of the Lax-Friedrichs type (LFt), Rusanov's method and the staggered and non-staggered second order Nessyahu-Tadmor (NT) schemes. Although these schemes are monotone or TVD, respectively, oscillations may be introduced at local data extrema. The dependence of oscillatory properties on the numerical viscosity coefficient is investigated rigorously for the LFt schemes, illuminating also the properties of Rusanov's method. It turns...
An analytic method for the initial value problem of the electric field system in vertical inhomogeneous anisotropic media
The time-dependent system of partial differential equations of the second order describing the electric wave propagation in vertically inhomogeneous electrically and magnetically biaxial anisotropic media is considered. A new analytical method for solving an initial value problem for this system is the main object of the paper. This method consists in the following: the initial value problem is written in terms of Fourier images with respect to lateral space variables, then the resulting problem...
An application of category theory to a class of the systems of the superquadratic wave equations.
An application of the theory of edge Sobolev spaces to weakly hyperbolic operators
An Approximation Theorem for Second-Order Evolution Equations.
An asymptotic expansion for the solution of the generalized Riemann problem. Part I : general theory
An asymptotic expansion for the solution of the generalized Riemann problem. Part 2 : application to the equations of gas dynamics
An effective method for the existence of the global attractor of a nonlinear wave equation.
An energy analysis of degenerate hyperbolic partial differential equations.
An energy analysis is carried out for the usual semidiscrete Galerkin method for the semilinear equation in the region (E) , subject to the initial and boundary conditions, on and . (E) is degenerate at and thus, even in the case , time derivatives of will blow up as . Also, in the case where is locally Lipschitz, solutions of (E) can blow up for in finite time. Stability and convergence of the scheme in is shown in the linear case without assuming (which can blow up as is...
An entropy satisfying scheme for two-layer shallow water equations with uncoupled treatment
We consider the system of partial differential equations governing the one-dimensional flow of two superposed immiscible layers of shallow water. The difficulty in this system comes from the coupling terms involving some derivatives of the unknowns that make the system nonconservative, and eventually nonhyperbolic. Due to these terms, a numerical scheme obtained by performing an arbitrary scheme to each layer, and using time-splitting or other similar techniques leads to instabilities in...
An error estimate for the parabolic approximation of multidimensional scalar conservation laws with boundary conditions
An existence result for balance laws with multifunctions: a model from the theory of granular media
We study an example of the balance law with a multifunction source term, coming from the theory of granular media. We prove the existence of "weak entropy solutions" to this system, using the vanishing viscosity method and compensated compactness. Because of the occurrence of a multifunction we give a new definition of the weak entropy solutions.
An existence theorem for an hyperbolic differential inclusion in Banach spaces
In this paper, we investigate the existence of solutions on unbounded domain to a hyperbolic differential inclusion in Banach spaces. We shall rely on a fixed point theorem due to Ma which is an extension to multivalued between locally convex topological spaces of Schaefer's theorem.
An explicit determination of the non-self-adjoint wave equations on curved space-time that satisfy Huygens' principle. Part I : Petrov type N background space-times
An explicit determination of the Petrov type N space-times on which the conformally invariant scalar wave equation satisfies Huygens' principle
An explicit determination of the space-times on which the conformally invariant scalar wave equation satisfies Huygens' principle. Part III : Petrov type III space-times