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Transactions of the American Mathematical Society

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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: 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).


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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.

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