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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
DOI: https://doi.org/10.1090/S0002-9939-2011-10801-3
Published electronically: January 24, 2011
MathSciNet review: 2811281
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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.


References [Enhancements On Off] (What's this?)

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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: https://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.

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