Thermal blow-up in a finite strip with superdiffusive properties

Colleen M. Kirk, W. Edward Olmstead

Research output: Contribution to journalArticlepeer-review

Abstract

We investigate the problem of a high-energy source localized within a one-dimensional superdiffusive medium of finite length. The problem is modeled by a fractional diffusion equation with a nonlinear source term. For the boundary conditions, we consider both the case of homogeneous Dirichlet conditions and the case of homogeneous Neumann conditions. We investigate this model to determine whether or not blow-up occurs. It is demonstrated that a blow-up may or may not occur for the Dirichlet case. On the other hand, a blow-up is unavoidable for the Neumann case.

Original languageEnglish (US)
Pages (from-to)949-959
Number of pages11
JournalFractional Calculus and Applied Analysis
Volume21
Issue number4
DOIs
StatePublished - Aug 1 2018

Keywords

  • fractional diffusion equation
  • nonlinear Volterra integral equations
  • superdiffusion
  • thermal blow-up

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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