Blow-up in a reactive-diffusive medium with a moving heat source

C. M. Kirk*, W Edward Olmstead

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

29 Scopus citations


A concentrated source of heat is allowed to move in one-dimension through a reactive-diffusive medium. For rather general motion, it is shown that if the speed remains sufficiently high then a blow-up can be avoided; whereas, if the speed remains sufficiently low then a blow-up must eventually occur. Other criteria involving the displacement and velocity of the heat source are found to guarantee a blow-up. Special examples of (i) rapid deceleration from one velocity level to a lower level and (ii) a simple periodic motion are examined.

Original languageEnglish (US)
Pages (from-to)147-159
Number of pages13
JournalZeitschrift fur Angewandte Mathematik und Physik
Issue number1
StatePublished - Jan 1 2002


  • Blowup
  • Integral equations
  • Moving heat sources

ASJC Scopus subject areas

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

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