An integro-differential conservation law arising in a model of granular flow

Debora Amadori, Wen Shen

Research output: Contribution to journalArticle

21 Scopus citations

Abstract

We study a scalar integro-differential conservation law which was recently derived by the authors as the slow erosion limit of a granular flow. Considering a set of more general erosion functions, we study the initial boundary value problem for which one cannot adapt the standard theory of conservation laws. We construct approximate solutions with a fractional step method, by recomputing the integral term at each time step. A priori L bound and total variation estimates yield the convergence and global existence of solutions with bounded variation. Furthermore, we present a well-posedness analysis which establishes that these solutions are stable in the L 1 norm with respect to the initial data.

Original languageEnglish (US)
Pages (from-to)105-131
Number of pages27
JournalJournal of Hyperbolic Differential Equations
Volume9
Issue number1
DOIs
StatePublished - Mar 1 2012

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics(all)

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