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

Abstract

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
Volume35
Issue number7
DOIs
StatePublished - Jul 1 2015

Fingerprint

Cell Migration
Similarity Solution
Second-order Ordinary Differential Equations
Existence and Uniqueness of Solutions
Neumann Boundary Conditions
Generalized Equation
Nonlinear Partial Differential Equations
Heat Equation
Partial differential equations
Substitution
Half line
Existence and Uniqueness
Partial differential equation
Ordinary differential equations
Substitution reactions
Boundary conditions
Model
Similarity
Generalization
Hot Temperature

Keywords

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

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics
  • Analysis

Cite this

Existence and uniqueness of similarity solutions of a generalized heat equation arising in a model of cell migration. / Stepien, Tracy L.; Smith, Hal.

In: Discrete and Continuous Dynamical Systems- Series A, Vol. 35, No. 7, 01.07.2015, p. 3203-3216.

Research output: Contribution to journalArticle

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