Existence and uniqueness of similarity solutions of a generalized heat equation arising in a model of cell migration

Tracy L. Stepien, Hal Smith

Research output: Contribution to journalArticle


We study similarity solutions of a nonlinear partial differential equation that is a generalization of the heat equation. Substitution of the similarity ansatz reduces the partial differential equation to a nonlinear second- order ordinary differential equation on the half-line with Neumann boundary conditions at both boundaries. The existence and uniqueness of solutions is proven using Wazewski's Principle.

Original languageEnglish (US)
Pages (from-to)3203-3216
Number of pages14
JournalDiscrete and Continuous Dynamical Systems- Series A
Issue number7
StatePublished - Jul 1 2015



  • Boundary value problem
  • Cell migration
  • Half-line
  • Neumann conditions
  • Similarity solution under scaling

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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