Thermal blow-up in a subdiffusive medium

W Edward Olmstead, Catherine A. Roberts

Research output: Contribution to journalArticle

17 Scopus citations

Abstract

The problem of thermal blow-up in a subdiffusive medium is examined within the framework of a fractional heat equation with a nonlinear source term. This model establishes that a thermal blow-up always occurs when a finite strip of subdiffusive material is exposed to the effects of a localized, high-energy source. This behavior is distinctly different from the classical diffusion case in which a blow-up can be avoided by locating the site, of the energy source, sufficiently close to one of the cold ends of the strip. The asymptotic growth of the solution near blow-up is determined for a nonlinear source whose output increases with temperature in either an algebraic or exponential manner. The blow-up growth rate is found to depend upon the anomalous diffusion parameter that defines the subdiffusive medium. This suggests that such media might be characterized by their response to a reaction-diffusion process.

Original languageEnglish (US)
Pages (from-to)514-523
Number of pages10
JournalSIAM Journal on Applied Mathematics
Volume69
Issue number2
DOIs
StatePublished - Dec 1 2008

Keywords

  • Asymptotic growth
  • Subdiffusion
  • Thermal blow-up
  • Volterra equation

ASJC Scopus subject areas

  • Applied Mathematics

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