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

Thomas Singer, Matias Vestberg

Research output: Contribution to journalArticleScientificpeer-review

11 Citations (Scopus)
46 Downloads (Pure)

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 languageEnglish
Pages (from-to)3014-3033
Number of pages20
JournalJournal of Differential Equations
Volume266
Issue number6
DOIs
Publication statusPublished - 5 Mar 2019
MoE publication typeA1 Journal article-refereed

Keywords

  • Doubly nonlinear parabolic equations
  • Local boundedness

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