Global existence of solutions to a coupled parabolic-hyperbolic system with moving boundary

Authors:
Y. S. Choi and Craig Miller

Journal:
Proc. Amer. Math. Soc. **139** (2011), 3257-3270

MSC (2010):
Primary 35K10, 35K59, 35L04

Published electronically:
January 24, 2011

MathSciNet review:
2811281

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A cell motility study leads to a moving boundary problem governed by a system of parabolic-hyperbolic equations. Establishing the parabolicity of one of the governing equations requires a priori bound analysis. Such bounds also exclude the formation of shock in the hyperbolic equation. Speeds of the moving boundaries can then be controlled, which eventually leads to the global existence of solutions.

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Additional Information

**Y. S. Choi**

Affiliation:
Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269-3009

Email:
choi@math.uconn.edu

**Craig Miller**

Affiliation:
Department of Mathematics, University of New Haven, 300 Boston Post Road, West Haven, Connecticut 06516

Email:
cmiller@newhaven.edu

DOI:
http://dx.doi.org/10.1090/S0002-9939-2011-10801-3

Keywords:
Global existence,
coupled parabolic-hyperbolic equations,
method of characteristics

Received by editor(s):
March 11, 2010

Received by editor(s) in revised form:
March 15, 2010, and August 9, 2010

Published electronically:
January 24, 2011

Communicated by:
Matthew J. Gursky

Article copyright:
© Copyright 2011
American Mathematical Society

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