Hyperbolic systems equivalent to the wave equation.
Hyperbolic systems of partial differential inclusions
-type contraction for systems of conservation laws
The semi-group associated with the Cauchy problem for a scalar conservation law is known to be a contraction in . However it is not a contraction in for any . Leger showed in [20] that for a convex flux, it is however a contraction in up to a suitable shift. We investigate in this paper whether such a contraction may happen for systems. The method is based on the relative entropy method. Our general analysis leads us to the new geometrical notion of Genuinely non-Temple systems. We treat in...
--Time decay estimate for solution of the Cauchy problem for hyperbolic partial differential equations of linear thermoelasticity
We prove the --time decay estimates for the solution of the Cauchy problem for the hyperbolic system of partial differential equations of linear thermoelasticity. In our proof based on the matrix of fundamental solutions to the system we use Strauss-Klainerman’s approach [12], [5] to the --time decay estimates.
Monotonicity of the number of passages in linear chains and of the basis reproduction number in epidemic models.
Necessary conditions for strong hyperbolicity of first order systems
Noncharacteristic mixed problems for hyperbolic systems of the first order [Book]
Nonlocal problem for the hyperbolic system of differential equation of the first order.
Nonlocal problems for quasilinear functional partial differential equations of first order.
Existence and uniqueness of almost everywhere solutions of nonlocal problems to functional partial differential systems in diagonal form are investigated. The proof is based on the characteristics and fixed point methods.
Normal forms of real symmetric systems with multiplicity
On -estimates for hyperbolic systems
On pseudosymmetric systems with one space variable
On the analysis of Bérenger’s perfectly matched layers for Maxwell’s equations
In this work, we investigate the Perfectly Matched Layers (PML) introduced by Bérenger [3] for designing efficient numerical absorbing layers in electromagnetism. We make a mathematical analysis of this model, first via a modal analysis with standard Fourier techniques, then via energy techniques. We obtain uniform in time stability results (that make precise some results known in the literature) and state some energy decay results that illustrate the absorbing properties of the model. This last...
On the analysis of Bérenger's Perfectly Matched Layers for Maxwell's equations
In this work, we investigate the Perfectly Matched Layers (PML) introduced by Bérenger [3] for designing efficient numerical absorbing layers in electromagnetism. We make a mathematical analysis of this model, first via a modal analysis with standard Fourier techniques, then via energy techniques. We obtain uniform in time stability results (that make precise some results known in the literature) and state some energy decay results that illustrate the absorbing properties of the model. This...
On the dynamics of the characteristic curves for the LSW model.
On the profiles of nonlinear geometric optics
Ondes soniques
Pointwise Fourier Inversion: a Wave Equation Approach.
Problèmes mixtes hyperboliques bien-posés
On présente une famille de problèmes mixtes hyperboliques linéaires bien-posés au sens de Hadamard. La nouveauté consiste à autoriser une perte de régularité entre les termes source et la solution. On montre ainsi que la condition de Lopatinskii faible est suffisante pour obtenir le caractère bien-posé des problèmes mixtes hyperboliques linéaires.
Radiation fields
We study the “hyperboloidal Cauchy problem” for linear and semi-linear wave equations on Minkowski space-time, with initial data in weighted Sobolev spaces allowing singular behavior at the boundary, or with polyhomogeneous initial data. Specifically, we consider nonlinear symmetric hyperbolic systems of a form which includes scalar fields with a nonlinearity, as well as wave maps, with initial data given on a hyperboloid; several of the results proved apply to general space-times admitting conformal...