Authors: Julien Jimenez Laurent Lévi
Publish Date: 2007/09/07
Volume: 60, Issue: 3-4, Pages: 319-335
Abstract
In this paper the mathematical analysis of a quasilinear parabolic–hyperbolic problem in a multidimensional bounded domain Ω is carried out In a region Ω p a diffusion–advection–reactiontype equation is set while in the complementary Ω h ≡ Ω Ω p only advection–reaction terms are taken into account First the definition of a weak solution u is provided through an entropy inequality on the whole domain Q by using the classical Kuzhkov entropy pairs and the F Otto framework to transcribe the boundary conditions on ∂Ω ∩ ∂Ω h Since Γ hp contains the outward characteristics for the firstorder operator set in Q h the uniqueness proof begins by focusing on the behavior of u in the hyperbolic layer and then in the parabolic one where u fulfills a variational equality that takes into account the entered data from Q h The existence property uses a vanishingviscosity method
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