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

Tracy L. Stepien; Hal Smith

doi:10.3934/dcds.2015.35.3203

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 journal › Article › peer-review

2 Scopus citations

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 language	English (US)
Pages (from-to)	3203-3216
Number of pages	14
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	35
Issue number	7
DOIs	https://doi.org/10.3934/dcds.2015.35.3203
State	Published - Jul 1 2015

Keywords

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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AB - 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.

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KW - Half-line

KW - Neumann conditions

KW - Similarity solution under scaling

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

Abstract

Keywords

ASJC Scopus subject areas

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