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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
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Additional information
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:
-
- 1.
- T. Hillen, A. Potapov, The one-dimensional chemotaxis model: global existence and asymptotic profile, Math. Methods Appl. Sci., 27(2004), 1783-1801. MR 2087297 (2005e:35100)
- 2.
- S. Kato, On local and global existence theorems for a nonautonomous differential equation in a Banach space, Funkcial. Ekvac., 19(1976), 279-286. MR 0440149 (55:13029)
- 3.
- H.A. Levine, B.D. Sleeman, A system of reaction diffusion equations arising in the theory of reinforced random walks, SIAM J. Appl. Math., 57(1997), 683-730. MR 1450846 (98g:35106)
- 4.
- H.A. Levine, B.D. Sleeman, M.N. Hamilton, Mathematical modeling of the onset of capillary formation initiating angiogenesis, J. Math. Biol., 42(2001), 195-238. MR 1828815 (2003b:92003)
- 5.
- T. Nishida, Nonlinear hyperbolic equations and related topics in fluid dynamics, Publ. Math., 1978. MR 0481578 (58:1690)
- 6.
- H.G. Othmer, A. Stevens, Aggregation, blowup, and collapse: the ABC's of taxis in reinforced random walks, SIAM J. Appl. Math., 57(1997), 1044-1081. MR 1462051 (99b:92001)
- 7.
- B.D. Sleeman, H.A. Levine, Partial differential equations of chemotaxis and angiogenesis, Math. Methods.
Appl. Sci., 24(2001), 405-426. MR 1821934 (2002c:92009) - 8.
- J. Smoller, Shock Waves and Reaction-Diffusion Equations, Springer-Verlag, New York-Berlin, 1983. MR 0688146 (84d:35002)
- 9.
- Y. Yang, H. Chen, W.A. Liu, On existence of global solutions and blow-up to a system of reaction-diffusion equations modelling chemotaxis, SIAM J. Math. Anal., 33(2001), 763-785. MR 1884721 (2003d:35159)
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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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