On global existence of solutions to a cross-diffusion system

Journal of Mathematical Analysis and Applications

Volumn 343, Issue 2, 2008, Pages 826-834

  Tuoc, Phan Van ^a  

^a UNIVERSITY OF MINNESOTA   (United States)

Author keywords

A priori estimates; Cross diffusion; Global existence; Gradient estimates; Nonlinear parabolic systems; Population dynamics; Self diffusion

Indexed keywords

EID: 41949088791     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2008.01.089     Document Type: Article

References (19)

1. Amann H. Dynamic theory of quasilinear parabolic equations - I. Abstract evolution equations. Nonlinear Anal. 12 9 (1988) 895-919
2. Amann H. Dynamic theory of quasilinear parabolic equations - II. Reaction-diffusion systems. Differential Integral Equations 3 1 (1990) 13-75
3. Amann H. Dynamic theory of quasilinear parabolic systems - III. Global existence. Math. Z. 202 (1989) 219-250
4. Amann H. Abstract methods in differential equations. Rev. R. Acad. Cienc. Ser. A Mat. 97 1 (2003) 89-105
5. Choi Y.S., Lui R., and Yamada Y. Existence of global solutions for the Shigesada-Kawasaki-Teramoto model with weak cross-diffusion. Discrete Contin. Dyn. Syst. 9 5 (2003) 1193-1200
6. Choi Y.S., Lui R., and Yamada Y. Existence of global solutions for the Shigesada-Kawasaki-Teramoto model with strongly coupled cross-diffusion. Discrete Contin. Dyn. Syst. 10 3 (2004) 719-730
7. DiBenedetto E. Degenerate Parabolic Equations (1993), Springer-Verlag, New York
8. Deuring P. An initial-boundary value problem for certain density-dependent diffusion system. Math. Z. 194 (1987) 375-396
9. Kim J.U. Smooth solutions to a quasilinear system of diffusion equations for certain population model. Nonlinear Anal. 8 (1984) 1121-1144
10. Ladyzenskaja O.A., Solonnikov V.A., and Ural'ceva N.N. Linear and Quasi-linear Equations of Parabolic Type. Transl. Math. Monogr. vol. 23 (1968), Amer. Math. Soc.
11. Le D. Global existence for a class of strongly coupled parabolic systems. Ann. Mat. Pura Appl. (4) 185 1 (2006) 133-154
12. Le D., and Nguyen T. Global existence for a class of triangular parabolic systems on domains of arbitrary dimension. Proc. Amer. Math. Soc. 133 7 (2005) 1985-1992
13. Le D., Nguyen L., and Nguyen T. Shigesada-Kawasaki-Teramoto model on higher dimensional domains. Electron. J. Differential Equations 72 (2003)
14. Li Y., and Zhao C. Global existence of solutions to a cross-diffusion system in higher dimensional domains. Discrete Contin. Dyn. Syst. 12 2 (2005) 185-192
15. Lou Y., Ni W.M., and Wu Y. On the global existence of a cross-diffusion system. Discrete Contin. Dyn. Syst. 4 2 (1998) 193-203
16. Tuoc P.V. Global existence of solutions to Shigesada-Kawasaki-Teramoto cross-diffusion systems on domains of arbitrary dimensions. Proc. Amer. Math. Soc. 135 12 (2007) 3933-3941
17. Shigesada N., Kawasaki K., and Teramoto E. Spatial segregation of interacting species. J. Theoret. Biol. 79 (1979) 83-89
18. Shim S.-A. Uniform boundedness and convergence of solutions to cross-diffusion systems. J. Differential Equations 185 1 (2002) 281-305
19. Yagi A. Global solution of some quasilinear parabolic systems in population dynamics. Nonlinear Anal. 21 (1993) 603-630