Critical speed for the avoidance of blow-up in a reactive-diffusive medium

W Edward Olmstead*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


A concentrated heat source moves at constant speed through a diffusive medium which can support an explosive reaction. If the conditions are such that a blow-up would occur for a stationary source, it is shown that there is a critical speed above which the explosion can be avoided. The reactive-diffusive medium is assumed to be contained in an infinitely long tube of general cross-section. Both the cases of Neumann and Dirichlet boundary conditions imposed on the tube surface are considered.

Original languageEnglish (US)
Pages (from-to)701-710
Number of pages10
JournalZeitschrift fur Angewandte Mathematik und Physik
Issue number5
StatePublished - Jan 1 1997


  • Blow up solutions
  • Integral equations

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)
  • Applied Mathematics

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