A simple construction of strong solutions to hyperbolic corner problems and an application

Une construction simple de solutions fortes pour les problèmes à coin hyperboliques et une application

Antoine Benoit (1)

1 LMPA - Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville

In this article we give a simple construction of strong solutions to hyperbolic corner problems. The main idea of the method is to reduce the analysis to the study of transport equations and to treat the coupling between the transport phenomena as a source term. Then we solve inductively with a loss of one derivative at each step. Such losses being compensated if one considers infinitely regular sources. This simple approach gives strong solutions to hyperbolic corner problems and thus answer a natural question. Indeed in a general setting such existence results are frequently not considered in the literature (we are here thinking to the seminal work of [10]). As an application of the existence of strong solutions, we study the viscous approximation of hyperbolic corner problems and we show that the boundary layers localized along the two sides of the boundary do not interact the one with the other.

Mots clés: Hyperbolic system of PDE; Boundary value problem; Corner domain; Viscous approximation; Existence of strong solutions

Domaines: Equations aux dérivées partielles [math.AP]

Antoine Benoit. A simple construction of strong solutions to hyperbolic corner problems and an application. 2024. ⟨hal-04702092⟩