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Register a new userLocal Boundedness of Weak Solutions to the Diffusive Wave Approximation of the Shallow Water Equations
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In this paper we prove that weak solutions to the Diffusive Wave Approximation of the Shallow Water equations $$ partial_t u - ablacdot ((u-z)^alpha| abla u|^{gamma-1} abla u) = f $$ 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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