Existence of traveling domain solutions for a two-dimensional moving boundary problem

Authors:
Y. S. Choi and Roger Lui

Journal:
Trans. Amer. Math. Soc. **361** (2009), 4027-4044

MSC (2000):
Primary 35R35, 92C17

DOI:
https://doi.org/10.1090/S0002-9947-09-04562-0

Published electronically:
March 20, 2009

MathSciNet review:
2500877

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we prove the existence of a traveling domain solution for a two-dimensional moving boundary problem. Specifically, we prove the existence of a domain that travels to the right at a constant speed and a function which solves a porous medium type equation in the domain with constant Dirichlet boundary condition. The proof is by Schaefer's fixed point theorem. The result may be viewed as an extension of the existence of traveling cell solutions of a one-dimensional cell motility model proved by the authors and Juliet Lee (2004).

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Additional Information

**Y. S. Choi**

Affiliation:
Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269

Email:
choi@math.uconn.edu

**Roger Lui**

Affiliation:
Department of Mathematical Sciences, Worcester Polytech Institute, Worcester, Massachusetts 01609

Email:
rlui@wpi.edu

DOI:
https://doi.org/10.1090/S0002-9947-09-04562-0

Keywords:
Cell motility,
moving boundary problem,
traveling domain solutions

Received by editor(s):
December 13, 2005

Received by editor(s) in revised form:
May 7, 2007

Published electronically:
March 20, 2009

Additional Notes:
The first author’s research was partially supported by NIH grant no. 5P41-RR013186-07

The second author’s research was partially supported by NSF grant no. DMS-0456570

Article copyright:
© Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.