Hyperbolic conservation laws on manifolds with limited regularity


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Lefloch P. G. , Okutmustur B.

COMPTES RENDUS MATHEMATIQUE, vol.346, pp.539-543, 2008 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 346
  • Publication Date: 2008
  • Doi Number: 10.1016/j.crma.2008.03.017
  • Title of Journal : COMPTES RENDUS MATHEMATIQUE
  • Page Numbers: pp.539-543

Abstract

We introduce a formulation of the initial and boundary value problem for nonlinear hyperbolic conservation laws posed on a differential manifold endowed with a volume form, possibly with a boundary; in particular, this includes the important case of Lorentzian manifolds. Only limited regularity is assumed on the geometry of the manifold. For this problem, we establish the existence and uniqueness of an L1 semi-group of weak solutions satisfying suitable entropy and boundary conditions.

We introduce a formulation of the initial and boundary value problem for nonlinear hyperbolic conservation laws posed on a differential manifold endowed with a volume form, possibly with a boundary; in particular, this includes the important case of Lorentzian manifolds. Only limited regularity is assumed on the geometry of the manifold. For this problem, we establish the existence and uniqueness of an L-1 semi-group of weak solutions satisfying suitable entropy and boundary conditions.