Thermal blow-up in a subdiffusive medium due to a nonlinear boundary flux

Colleen M. Kirk, W. Edward Olmstead

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


A fractional heat equation is used to model thermal diffusion in a one-dimensional bar that exhibits subdiffusive behavior. The left end of the bar is subjected to a nonlinear influx of heat. For the boundary constraint at the right end of the bar, two cases are considered, namely a homogeneous Neumann condition and a homogeneous Dirichlet condition. By reducing both cases to a nonlinear Volterra equation, it is shown that a blow-up always occurs. The asymptotic behavior near the blow-up is determined for both cases. It is also shown that the solution for the Neumann case dominates that of the Dirichlet case.

Original languageEnglish (US)
Pages (from-to)191-205
Number of pages15
JournalFractional Calculus and Applied Analysis
Issue number1
StatePublished - Mar 2014


  • blow-up
  • fractional heat equation
  • nonlinear Volterra integral equations
  • subdiffusion

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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