On the $L^2$ well posedness of Hyperbolic Initial Boundary Value Problems
Language
en
Document de travail - Pré-publication
English Abstract
In this paper we give a class of hyperbolic systems, which includes systems with constant mutliplicities but significantly wider, for which the initial boundary value problem with source term and initial and boundary data ...Read more >
In this paper we give a class of hyperbolic systems, which includes systems with constant mutliplicities but significantly wider, for which the initial boundary value problem with source term and initial and boundary data in $L^2$, is well posed in $L^2$, provided that the necessary uniform Lopatinski condition is satisfied. Moreover, the speed of propagation is the speed of the interior problem. In the opposite direction, we show on an example that, even for symmetric systems in the sense of Friedrichs, with variable coefficients and variable multiplicities, the uniform Lopatinski condition is not sufficient to ensure the well posedness of the IBVP.Read less <
English Keywords
initial boundary value problems
Hyperbolic
systems of partial differential equations
symmerizers
energie estimate
finite speed of propgagation
Origin
Hal imported