Coupled Volterra equations with blow-up solutions

W. E. Olmstead, Catherine A. Roberts, Keng Deng

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

A pair of coupled nonlinear Volterra equations are examined for possible blow-up solutions. The system is motivated by certain models of explosion phenomena in a diffusive medium. Criteria for a blow-up to occur as well as bounds on the time of its occurrence are derived for a general class of nonlinearities. Specific results are obtained for two special cases involving power law and exponential nonlinearities. Also, the asymptotic growth rate near blow-up is determined for these two special cases when the kernel behaves like that of the one-dimension heat equation.

Original languageEnglish (US)
Pages (from-to)499-516
Number of pages18
JournalJournal of Integral Equations and Applications
Volume7
Issue number4
DOIs
StatePublished - 1995

ASJC Scopus subject areas

  • Numerical Analysis
  • Applied Mathematics

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