Global existence of solutions to a coupled parabolichyperbolic system with moving boundary
Authors:
Y. S. Choi and Craig Miller
Journal:
Proc. Amer. Math. Soc. 139 (2011), 32573270
MSC (2010):
Primary 35K10, 35K59, 35L04
Published electronically:
January 24, 2011
MathSciNet review:
2811281
Fulltext PDF
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Additional Information
Abstract: A cell motility study leads to a moving boundary problem governed by a system of parabolichyperbolic 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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 Y.S. Choi and R. Lui, Linearized stability of traveling cell solutions arising from a moving boundary problem. Proc. Amer. Math. Soc. 135 (2007), 743753. MR 2262870 (2007h:37119)
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 Y.S. Choi and R. Lui, Existence of traveling domain solutions for a twodimensional moving boundary problem, Trans. Amer. Math. Soc. 361 (2009), 40274044. MR 2500877 (2010j:35623)
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 T.D. Pollard and G.G. Borisy, Cellular motility driven by assembly and disassembly of actin filaments, Cell, 112 (2003), 453465.
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 M. Protter and H.F. Weinberger, Maximum Principles in Differential Equations, PrenticeHall, Englewood Cliffs, NJ, 1967. MR 0219861 (36:2935)
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 S.M. Rafelski and J.A. Theriot, Crawling toward a unified model of cell mobility: Spatial and temporal regulation of actin dynamics, Annual Rev. Biochem. 73 (2004), 20939.
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Additional Information
Y. S. Choi
Affiliation:
Department of Mathematics, University of Connecticut, Storrs, Connecticut 062693009
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/S000299392011108013
Keywords:
Global existence,
coupled parabolichyperbolic 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.
