Local boundedness of weak solutions to the Diffusive Wave Approximation of the Shallow Water equations

Thomas Singer; Matias Vestberg

doi:10.1016/j.jde.2018.08.051

Local boundedness of weak solutions to the Diffusive Wave Approximation of the Shallow Water equations

Thomas Singer, Matias Vestberg

Department of Mathematics and Systems Analysis

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Abstract

In this paper we prove that weak solutions to the Diffusive Wave Approximation of the Shallow Water equations ∂tu−∇⋅((u−z)α|∇u|γ−1∇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.

Original language	English
Pages (from-to)	3014-3033
Number of pages	20
Journal	Journal of Differential Equations
Volume	266
Issue number	6
DOIs	https://doi.org/10.1016/j.jde.2018.08.051
Publication status	Published - 5 Mar 2019
MoE publication type	A1 Journal article-refereed

Keywords

Doubly nonlinear parabolic equations
Local boundedness

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10.1016/j.jde.2018.08.051

SCI_Singer_Vestberg_Local_BoundednessAccepted author manuscript, 367 KBLicence: CC BY-NC-ND

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abstract = "In this paper we prove that weak solutions to the Diffusive Wave Approximation of the Shallow Water equations ∂tu−∇⋅((u−z)α|∇u|γ−1∇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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N2 - In this paper we prove that weak solutions to the Diffusive Wave Approximation of the Shallow Water equations ∂tu−∇⋅((u−z)α|∇u|γ−1∇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.

AB - In this paper we prove that weak solutions to the Diffusive Wave Approximation of the Shallow Water equations ∂tu−∇⋅((u−z)α|∇u|γ−1∇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.

KW - Doubly nonlinear parabolic equations

KW - Local boundedness

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JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 6

ER -

Local boundedness of weak solutions to the Diffusive Wave Approximation of the Shallow Water equations

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Keywords

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