Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Global existence of solutions to Shigesada-Kawasaki-Teramoto cross-diffusion systems on domains of arbitrary dimensions

Author(s): Phan Van Tuôc
Journal: Proc. Amer. Math. Soc. 135 (2007), 3933-3941.
MSC (2000): Primary 35B50, 35K50, 35K55, 35K57
Posted: August 2, 2007
MathSciNet review: 2341943
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: We consider a strongly coupled nonlinear parabolic system which arises in population dynamics in -dimensional domains ( $n\geq 1$ ). Global existence of classical solutions under certain restrictions on the coefficients is established.

References:

1.: H. Amann, Dynamic theory of quasilinear parabolic equations - I. Abstract evolution equations, Nonlinear Analysis - Theory, Methods and Applications, Vol. 12, 9(1988), 895-919. MR 960634 (89j:35072)
2.: H. Amann, Dynamic theory of quasilinear parabolic equations - II. Reaction-diffusion systems, Differential Integral Equations, Vol. 3, 1(1990), 13-75. MR 1014726 (90i:35124)
3.: H. Amann, Dynamic theory of quasilinear parabolic systems - III. Global existence, Math. Z. 202(1989), 219-250. MR 1013086 (90i:35125)
4.: H. Amann, Abstract methods in differential equations, Rev. R. Acad. Cien. Serie A. Mat. Vol. 97, 1(2003), 89-105. MR 2037227 (2004k:35231)
5.: Y.S. Choi, R. Lui and Y. Yamada, Existence of global solutions for the Shigesada-Kawasaki-Teramoto model with weak cross-diffusion, Discrete and Continuous Dynamical Systems, Vol. 9, 5(2003), 1193-1200. MR 1974423 (2004b:35145)
6.: Y.S. Choi, R. Lui and Y. Yamada, Existence of global solutions for the Shigesada-Kawasaki-Teramoto model with strongly coupled cross-diffusion, Discrete and Continuous Dynamical Systems, Vol. 10, 3(2004), 719-730. MR 2018876 (2005e:35099)
7.: E. DiBenedetto, Degenerate Parabolic Equations, Springer-Verlag, New York, 1993. MR 1230384 (94h:35130)
8.: A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, N.J., 1964. MR 0181836 (31:6062)
9.: O.A. Ladyzenskaja, V.A. Solonnikov and N.N. Ural'ceva, Linear and Quasi-linear Equations of Parabolic Type, Translations of Mathematical Monographs, 23, AMS, 1968. MR 0241821 (39:3159a)
10.: G. Lieberman, Second Order Parabolic Differential Equations, World Scientific, 1996. MR 1465184 (98k:35003)
11.: D. Le and T. Nguyen, Global existence for a class of triangular parabolic systems on domains of arbitrary dimension, Proceedings of AMS, Vol. 133, 7(2005), 1985-1992. MR 2137864 (2005k:35215)
12.: Y. Li and C. Zhao, Global existence of solutions to a cross-diffusion system in higher dimensional domains, Discrete and Continuous Dynamical Systems, Vol. 12, 2(2005), 185-192. MR 2122161 (2005i:35147)
13.: Y. Lou, W.M. Ni and Y. Wu, On the global existence of cross-diffusion systems, Discrete and Continuous Dynamical Systems, Vol. 4, 2(1998), 193-203. MR 1616969 (99f:35089)
14.: M.H. Protter and H.F. Weinberger, Maximum Principles in Differential Equations, Second Edition, Springer-Verlag, New York, 1984. MR 762825 (86f:35034)
15.: N. Shigesada, K. Kawasaki and E. Teramoto, Spatial segregation of interacting species, J. Theoretical Biology, 79(1979), 83-89. MR 540951 (80e:92038)
16.: J. Smoller, Shock Waves and Reaction-Diffusion Equations. Springer, New York (1983).

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