Volterra equations which model explosion in a diffusive medium

Catherine A. Roberts, D. Glenn Lasseigne, W. E. Olmstead

Research output: Contribution to journalArticlepeer-review

44 Scopus citations

Abstract

An investigation is made of certain nonlinear Volterra integral equations which model explosive behavior in a diffusive medium. The basic results provide criteria involving the kernel and the nonlinearity for the solution to experience blow-up. Supporting examples from solid combustion and shear band formation are provided. Also, the connection is made with one-dimensional parabolic partial differential equations.

Original languageEnglish (US)
Pages (from-to)531-546
Number of pages16
JournalJournal of Integral Equations and Applications
Volume5
Issue number4
DOIs
StatePublished - 1993

ASJC Scopus subject areas

  • Numerical Analysis
  • Applied Mathematics

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