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arXiv · 1806.04462

Local Boundedness of Weak Solutions to the Diffusive Wave Approximation of the Shallow Water Equations

Thomas Singer·Matias Vestberg
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Abstract

In this paper we prove that weak solutions to the Diffusive Wave Approximation of the Shallow Water equations $$ \partial_t u - \nabla\cdot ((u-z)^\alpha|\nabla u|^{\gamma-1}\nabla u) = f $$ are locally bounded. Here, $u$ describes the height of the water, $z$ is a given function that represents the land elevation and $f$ is a source term accounting for evaporation, infiltration or rainfall.

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Thomas Singer, Matias Vestberg. 2018-06-12. Local Boundedness of Weak Solutions to the Diffusive Wave Approximation of the Shallow Water Equations. https://arxiv.org/abs/1806.04462

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