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Global existence of solutions to a hyperbolic-parabolic system
Author(s):
Mei
Zhang;
Changjiang
Zhu
Journal:
Proc. Amer. Math. Soc.
135
(2007),
1017-1027.
MSC (2000):
Primary 35K20, 35K55, 35L50
Posted:
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  -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.
References:
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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:
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
Posted:
September 18, 2006
Communicated by:
Walter Craig
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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