On equivalence of entropy and viscosity solutions to degenerate parabolic equations and applications

2024/08/09 by Hiroyoshi Mitake, Hiroshi Watanabe, Mitake, Hiroyoshi +1
Mathematics · Engineering · #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2408.04960

Abstract

Here, we consider anisotropic degenerate parabolic-hyperbolic equations and degenerate quasilinear Hamilton-Jacobi equations. We prove the equivalence of two notions of entropy and viscosity solutions of two equations, and apply it to obtain a large-time behavior of viscosity solutions to quasilinear Hamilton-Jacobi equations, and entropy solutions to degenerate parabolic-hyperbolic equations in a periodic setting.

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