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

Tracy L. Stepien; Hal L. Smith

doi:10.3934/dcds.2015.35.3203

Article Contents

2015, Volume 35, Issue 7: 3203-3216. Doi: 10.3934/dcds.2015.35.3203

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

Tracy L. Stepien^1, and
Hal L. Smith^2,

1.
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260
2.
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287-1804

Received: May 31, 2014

Revised: November 30, 2014

Published: May 2017

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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 Ważewski's Principle.

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Mathematics Subject Classification: Primary: 35C06, 34B40, 34B15; Secondary: 35Q92.

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