Renormalized entropy solutions of homogeneous Dirichlet problems for quasilinear anisotropic degenerate parabolic-hyperbolic equations

By Yachun Li, Qin Wang. Advances in Differential Equations, 2012

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The aim of this paper is to prove the well-posedness (existence and uniqueness) of entropy solutions to the general anisotropic degenerate parabolic–hyperbolic equations with L∞ initial data and homogeneous Dirichlet boundary condition. We use the doubling variables device to prove a comparison theorem, which implies the uniqueness. The existence of entropy solutions can be obtained by finding the limit of solutions for the regularized equation of strictly parabolic type.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

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