hal-00475852, version 1

Scalar conservation laws with nonlinear boundary conditions

Boris Andreianov () ^1, 2, Karima Sbihi () ^1, 3

C. R. Math. Acad. Sci. Paris 345, 8 (2007) 431-434

• 1:  Laboratoire de Mathématiques (LM-Besançon)
• http://www-math.univ-fcomte.fr/
  CNRS : UMR6623 – Université de Franche-Comté UFR Sciences et techniques 16 route de Gray 25 030 Besançon cedex France
• 2:  Université de Franche-Comté (Laboratoire de Mathématiques)
• 
  Université de Franche-Comté Laboratoire de Mathématiques Université de Franche-Comté 16 route de Gray 25030 Besançon Cedex France
• 3:  Institut de Recherche Mathématique Avancée (IRMA)
• http://www-irma.u-strasbg.fr/
  CNRS : UMR7501 – Université de Strasbourg 7 rue René-Descartes, 67084 Strasbourg Cedex, France France

Bibliographic reference

• Type of document: Articles in peer-reviewed journal
• Subject: Mathematics/Analysis of PDEs
• Title: Scalar conservation laws with nonlinear boundary conditions
• Abstract: This Note deals with uniqueness and continuous dependence of solutions to the problem u_t + div ϕ(u) = f on (0,T ) ×Ω with initial condition u(0, ·) = u_0 on Ω and with (formal) nonlinear boundary conditions ϕ(u) · ν ∈ β(t,x,u) on (0,T ) × ∂Ω, where β(t,x, ·) stands for a maximal monotone graph on R. We suggest an interpretation of the formal boundary condition which generalizes the Bardos–LeRoux–Nédélec condition, and introduce the corresponding notions of entropy and entropy process solutions using the strong trace framework of E.Yu. Panov. We prove uniqueness and provide some support for our interpretation of the boundary condition.
• Fulltext language: English
• Production date: 2007-06-27
• DOI: 10.1016/j.crma.2007.09.008
• Journal: C. R. Math. Acad. Sci. Paris
• Audience: international
• Publication date: 2007
• Volume: 345
• Issue: 8
• Page, identifiant, ...: 431–434
• Classification: 35L65

• hal-00475852, version 1
• http://hal.archives-ouvertes.fr/hal-00475852
• oai:hal.archives-ouvertes.fr:hal-00475852
• From: Boris Andreianov <>
• Submitted on: Friday, 23 April 2010 10:48:49
• Updated on: Friday, 23 April 2010 10:48:49