Blow-up in a subdiffusive medium with advection

W. Edward Olmstead, Colleen M. Kirk, Catherine A. Roberts

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


A mathematical model is presented for a localized energy source in a subdiffusive medium with advection. It is shown that blow-up cannot be prevented, regardless of the advection speed. This result holds for media associated with an unbounded spatial domain in one, two, or three dimensions. Results also suggest that increasing the advection speed will delay the time to blow-up, even though it does not prevent a blow-up. It is interesting to note that these results are in distinct contrast with the analogous classical diffusion problem, in which blow-up can be prevented by increasing sufficiently the advection speed. The asymptotic behavior of the temperature near the blow-up time is also presented.

Original languageEnglish (US)
Pages (from-to)1655-1667
Number of pages13
JournalDiscrete and Continuous Dynamical Systems
Issue number4
StatePublished - Dec 2010


  • Advection
  • Blow-up
  • Heat equation
  • Moving source
  • Subdiffusion

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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