Skip to main content
Article
Existence of Traveling Domain Solutions for a Two-Dimensional Moving Boundary Problem
Transactions of the American Mathematical Society
  • Y. S. Choi
  • Roger Lui, Worcester Polytechnic Institute
Document Type
Article
Publication Date
8-1-2009
Disciplines
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 k and a function b 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).

DOI
10.1090/S0002-9947-09-04562-0
Publisher Statement
First published in Transactions of the American Mathematical Society in 361(8), published by the American Mathematical Society.
Citation Information
Y. S. Choi and Roger Lui. "Existence of Traveling Domain Solutions for a Two-Dimensional Moving Boundary Problem" Transactions of the American Mathematical Society Vol. 361 Iss. 8 (2009) p. 4027 - 4044
Available at: http://works.bepress.com/roger_lui/9/