Existence of Solutions to a Diffusive Shallow Medium Equation

2020/01/22 by Bögelein, Verena, Dietrich, Nicolas, Vestberg, Matias · 2 citations
#35D30 #35K20 #35K65 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2001.07942

Abstract

In this article we establish the existence of weak solutions to the shallow medium equation. We proceed by an approximation argument. First we truncate the coefficients of the equation from above and below. Then we prove convergence of the solutions of the truncated problem to a solution to the original equation.

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• A non-negativity-preserving cut-cell discontinuous Galerkin method for the diffusive wave equation
• Existence, comparison principle and uniqueness for fully nonlinear anisotropic evolution equations

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