Existence of traveling domain solutions for a two-dimensional moving boundary problem
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- by Y. S. Choi and Roger Lui PDF
- Trans. Amer. Math. Soc. 361 (2009), 4027-4044 Request permission
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).References
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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
- MR Author ID: 116795
- Email: rlui@wpi.edu
- 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 - © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2500877