Existence and stability of traveling waves for an integro-differential equation for slow erosion

Graziano Guerra, Wen Shen

Research output: Contribution to journalArticle

7 Scopus citations

Abstract

We study an integro-differential equation that describes the slow erosion of granular flow. The equation is a first order nonlinear conservation law where the flux function includes an integral term. We show that there exist unique traveling wave solutions that connect profiles with equilibrium slope at ±∞. Such traveling waves take very different forms from those in standard conservation laws. Furthermore, we prove that the traveling wave profiles are locally stable, i.e., solutions with monotone initial data approach the traveling waves asymptotically as t→ + ∞.

Original languageEnglish (US)
Pages (from-to)253-282
Number of pages30
JournalJournal of Differential Equations
Volume256
Issue number1
DOIs
StatePublished - Jan 1 2014

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Existence and stability of traveling waves for an integro-differential equation for slow erosion'. Together they form a unique fingerprint.

  • Cite this