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. To cite this article: B. Andreianov, K. Sbihi, C. R. Acad. Sci. Paris, Ser. I 345 (2007).
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