hal-00121715, version 1

Uniqueness for multidimensional hyperbolic systems with commuting Jacobians

Hermano Frid () ¹, Philippe G. Le Floch () ²

• 1:  Instituto Nacional de Matemática Pura e Aplicada (IMPA)
• http://www.impa.br/opencms/pt/
  Instituto Nacional de matematica pura e aplicada Estrada Dona Castorina 110 Rio de Janeiro 22460-320 Brazil
• 2:  Laboratoire Jacques-Louis Lions (LJLL)
• http://www.ann.jussieu.fr
  CNRS : UMR7598 – Université Pierre et Marie Curie [UPMC] - Paris VI B.C. 187 75252 Paris Cedex 05 France

Bibliographic reference

• Type of document: Documents without publication reference (Preprint)
• Subject: Mathematics/Numerical Analysis
• Title: Uniqueness for multidimensional hyperbolic systems with commuting Jacobians
• Abstract: We consider nonlinear hyperbolic systems of conservation laws in several space dimensions whose Jacobian matrices commute and, more generally, systems that need not be conservative. Generalizing a theorem by Bressan and LeFloch for one-dimensional systems, we establish that the Cauchy problem admits at most one entropy solution depending continuously upon its initial data. The uniqueness result is proven within the class (introduced here) of locally regular BV functions with locally controled oscillation. These regularity conditions are modeled on well-known properties in the one-dimensional case. Our uniqueness theorem also improves upon the known results for one-dimensional systems.
• Fulltext language: English

Attached file list to this document: 

• hal-00121715, version 1
• http://hal.archives-ouvertes.fr/hal-00121715
• oai:hal.archives-ouvertes.fr:hal-00121715
• From: Pascal Joly <>
• Submitted on: Thursday, 21 December 2006 16:06:48
• Updated on: Thursday, 21 December 2006 16:22:30