Singularity analysis of a reaction-diffusion equation with a solution-dependent Dirac delta source

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Abstract

We analyze the existence and singularity of a solution to a reaction-diffusion equation, whose reaction term is represented by a Dirac delta function which depends on the solution itself. We prove that there exists a unique analytic solution with a logarithmic singularity at the origin.

Original languageEnglish
Pages (from-to)2179-2183
Number of pages5
JournalApplied Mathematics Letters
Volume25
Issue number12
DOIs
StatePublished - Dec 2012

Keywords

  • Diffusion
  • Dirac delta function
  • Reaction
  • Singularity

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