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Article Dans Une Revue Comptes rendus de l'Académie des sciences. Série I, Mathématique Année : 2007

Scalar conservation laws with nonlinear boundary conditions

Résumé

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.

Dates et versions

hal-00475852 , version 1 (23-04-2010)

Identifiants

Citer

Boris Andreianov, Karima Sbihi. Scalar conservation laws with nonlinear boundary conditions. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2007, 345 (8), pp.431-434. ⟨10.1016/j.crma.2007.09.008⟩. ⟨hal-00475852⟩
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