A note on the existence of L 2 valued solutions for a hyperbolic system with boundary conditions
Marchesani, Stefano; Olla, Stefano (2020), A note on the existence of L 2 valued solutions for a hyperbolic system with boundary conditions. https://basepub.dauphine.fr/handle/123456789/18457
TypeDocument de travail / Working paper
External document linkhttps://hal.archives-ouvertes.fr/hal-01920905v1
Cahier de recherche CEREMADE, Université Paris-Dauphine
Series titleCahier de recherche CEREMADE, Université Paris-Dauphine
MetadataShow full item record
Gran Sasso Science Institute [GSSI]
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)We prove existence of L2-weak solutions of a quasilinear wave equation with boundary conditions. This is done using a vanishing viscosity approximation with mixed Dirichlet-Neumann boundary conditions. In this settingwe obtain a uniform a priori estimate in L2, allowing us to use L2 Young measures, together with the classical tools of compensated compactness. We then prove that the viscous solutions converge to weak solutions of the quasili near wave equation strongly in Lp, for any p∈[1, 2), that satisfy, in a weak sense, the boundary conditions in the sense given by Definition 2.1.Furthermore, Clausius inequality is in force for these solutions.
Subjects / Keywordshyperbolic conservation laws; boundary conditions; weak solutions; vanishing viscosity,; compensated compactness
Showing items related by title and author.
Dissipative boundary conditions for 2 × 2 hyperbolic systems of conservation laws for entropy solutions in BV Coron, Jean-Luc; Ervedoza, Sylvain; Ghoshal, Shyam; Glass, Olivier; Perrollaz, Vincent (2017) Article accepté pour publication ou publié