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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Global existence of solutions to a hyperbolic-parabolic system


Authors: Mei Zhang and Changjiang Zhu
Journal: Proc. Amer. Math. Soc. 135 (2007), 1017-1027
MSC (2000): Primary 35K20, 35K55, 35L50
Published electronically: September 18, 2006
MathSciNet review: 2262902
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Abstract: In this paper, we investigate the global existence of solutions to a hyperbolic-parabolic model of chemotaxis arising in the theory of reinforced random walks. To get $ L^2$-estimates of solutions, we construct a nonnegative convex entropy of the corresponding hyperbolic system. The higher energy estimates are obtained by the energy method and a priori assumptions.


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Additional Information

Mei Zhang
Affiliation: Laboratory of Nonlinear Analysis, Department of Mathematics, Central China Normal University, Wuhan 430079, People’s Republic of China

Changjiang Zhu
Affiliation: Laboratory of Nonlinear Analysis, Department of Mathematics, Central China Normal University, Wuhan 430079, People’s Republic of China
Email: cjzhu@mail.ccnu.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08773-9
PII: S 0002-9939(06)08773-9
Keywords: Hyperbolic-parabolic system, {\it a priori} estimates, entropy-entropy flux, global existence.
Received by editor(s): October 19, 2005
Published electronically: September 18, 2006
Communicated by: Walter Craig
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.