Optimality conditions for a Bolza problem governed by a hyperbolic system of Darboux-Goursat type
Periodic solutions of a weakly nonlinear wave equation
Propriété de symétrie des matrices localisées d'une matrice fortement hyperbolique en un point multiple
Remarks on weak stabilization of semilinear wave equations
If a second order semilinear conservative equation with esssentially oscillatory solutions such as the wave equation is perturbed by a possibly non monotone damping term which is effective in a non negligible sub-region for at least one sign of the velocity, all solutions of the perturbed system converge weakly to 0 as time tends to infinity. We present here a simple and natural method of proof of this kind of property, implying as a consequence some recent very general results of Judith Vancostenoble....
Remarks on weak stabilization of semilinear wave equations
If a second order semilinear conservative equation with esssentially oscillatory solutions such as the wave equation is perturbed by a possibly non monotone damping term which is effective in a non negligible sub-region for at least one sign of the velocity, all solutions of the perturbed system converge weakly to 0 as time tends to infinity. We present here a simple and natural method of proof of this kind of property, implying as a consequence some recent very general results of Judith Vancostenoble. ...
Remarques sur les systèmes fortement hyperboliques
Riesz basis property of Timoshenko beams with boundary feedback control.
Rigorous derivation of Korteweg-de Vries-type systems from a general class of nonlinear hyperbolic systems
Rigorous derivation of Korteweg-de Vries-type systems from a general class of nonlinear hyperbolic systems
In this paper, we study the long wave approximation for quasilinear symmetric hyperbolic systems. Using the technics developed by Joly-Métivier-Rauch for nonlinear geometrical optics, we prove that under suitable assumptions the long wave limit is described by KdV-type systems. The error estimate if the system is coupled appears to be better. We apply formally our technics to Euler equations with free surface and Euler-Poisson systems. This leads to new systems of KdV-type.
Scattering theory for a nonlinear system of wave equations with critical growth
We consider scattering properties of the critical nonlinear system of wave equations with Hamilton structure ⎧uₜₜ - Δu = -F₁(|u|²,|v|²)u, ⎨ ⎩vₜₜ - Δv = -F₂(|u|²,|v|²)v, for which there exists a function F(λ,μ) such that ∂F(λ,μ)/∂λ = F₁(λ,μ), ∂F(λ,μ)/∂μ = F₂(λ,μ). By using the energy-conservation law over the exterior of a truncated forward light cone and a dilation identity, we get a decay estimate for the potential...
Solutions globales de systèmes non linéaires sur des variétés hyperboliques
Some boundary value problems for systems of linear partial differential equations of hyperbolic type.
Stability for a coupled system of wave equations of Kirchhoff type with nonlocal boundary conditions.
Symétrisabilité des matrices localisées d'une matrice fortement hyperbolique en un point multiple
Systèmes faiblement hyperboliques
Systèmes hyperboliques à caractéristiques de multiplicité variable
The Dirichlet boundary value problem for the system uxi-xj=0, j≠i.
Uniform stabilization for elastic waves system with highly nonlinear localized dissipation.
Uniform stabilization for the Timoshenko beam by a locally distributed damping.
Unique solvability of initial boundary-value problems for hyperbolic systems in cylinders whose base is a cusp domain.