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We consider the general degenerate hyperbolic-parabolic equation: ut + div f (u) − ∆φ(u) = 0 in Q = (0, T) × Ω, T > 0, Ω ⊂ R N ; (E) with initial condition and the zero flux boundary condition. Here φ is a continuous non decreasing function. Following [Bürger, Frid and Karlsen, J. Math. Anal. Appl, 2007], we assume that f is compactly supported (this is the… (More)
We study a Robin boundary problem for degenerate parabolic equation. We suggest a notion of entropy solution and propose a result of existence and uniqueness. Numerical simulations illustrate some aspects of solution behaviour. Monodimensional experiments are presented.
We study a degenerate parabolic-hyperbolic equation with zero flux boundary condition. The aim of this paper is to prove convergence of numerical approximate solutions towards the unique entropy solution. We propose an implicit finite volume scheme on admissible mesh.We establish fundamental estimates and prove that the approximate solution converge towards… (More)