Approximation of initial and boundary value problems for quasilinear first order equations
Arbitrary Lagrangian Eulerian method for compressible plasma simulations
Asymptotic behaviour in time of solutions to some equations generalizing the Korteweg-de Vries-Burgers equation
Behavior of critical solutions of a nonlocal hyperbolic problem in Ohmic heating of foods.
Blow-Up of Solutions of Nonlinear Wave Equations in Three Space Dimensions.
Blow-Up Theorems for Nonlinear Wave Equations.
Blow-up time estimates for a non-local reactive-convective problem modelling sterilization of food
Blow-up time estimates for a non-local reactive-convective problem modelling sterilization of food
Boundary layers and glancing blow-up in nonlinear geometric optics
Boundary values and the transformation problem for constant principal strain mappings.
Branching random motions, nonlinear hyperbolic systems and travellind waves
A branching random motion on a line, with abrupt changes of direction, is studied. The branching mechanism, being independent of random motion, and intensities of reverses are defined by a particle's current direction. A solution of a certain hyperbolic system of coupled non-linear equations (Kolmogorov type backward equation) has a so-called McKean representation via such processes. Commonly this system possesses travelling-wave solutions. The convergence of solutions with Heaviside terminal...
Characterizations of the ranges of some nonlinear operators and applications to boundary value problems
Classical conormal, semilinear waves
Coherent and focusing multidimensional nonlinear geometric optics
Coherent nonlinear waves and the Wiener algebra
We study oscillatory solutions of semilinear first order symmetric hyperbolic system , with real analytic .The main advance in this paper is that it treats multidimensional problems with profiles that are almost periodic in with only the natural hypothesis of coherence.In the special case where has constant coefficients and the phases are linear, the solutions have asymptotic descriptionwhere the profile is almost periodic in .The main novelty in the analysis is the space of profiles which...
Compacité par compensation trilinéaire et optique géométrique non linéaire
Continuity of solutions of a quasilinear hyperbolic equation with hysteresis
This paper is devoted to the investigation of quasilinear hyperbolic equations of first order with convex and nonconvex hysteresis operator. It is shown that in the nonconvex case the equation, whose nonlinearity is caused by the hysteresis term, has properties analogous to the quasilinear hyperbolic equation of first order. Hysteresis is represented by a functional describing adsorption and desorption on the particles of the substance. An existence result is achieved by using an approximation of...
Continuous solutions of the problem of a string vibrating against an obstacle
Convergence analysis of finite difference schemes for semi-linear initial-value problems
Convergence d'un schéma décentré amont sur un maillage triangulaire pour un problème hyperbolique linéaire