Uniform boundedness and convergence of solutions to the systems with cross-diffusions dominated by self-diffusions

Nonlinear Analysis: Real World Applications

Volumn 4, Issue 1, 2003, Pages 65-86

  Shim, Seong A ^a,b  

^a UNIVERSITY OF MINNESOTA   (United States)

^b MCMASTER UNIVERSITY   (Canada)

Author keywords

Convergence; Cross diffusion; Self diffusion; Uniform bound

Indexed keywords

EID: 0037332647     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1468-1218(02)00014-7     Document Type: Article

References (14)

1. R.A. Adams, Sobolev Spaces, Academic Press, New York, 1975.
2. H. Amann, Dynamic theory of quasilinear parabolic equations, III. Global Existence, Math. Z. 202 (1989) 219-250.
3. H. Amann, Dynamic theory of quasilinear parabolic equations, II. Reaction-diffusion systems, Differential Integral Equations 3 (1) (1990) 13-75.
4. H. Amann, Non-homogeneous linear and quasilinear elliptic and parabolic boundary value problems, Function Spaces, Differential Operators and Nonlinear Analysis (Friedrichroda, 1992), Teubner-Texte Math., Vol. 133, Teubner, Stuttgart, 1993, pp. 9-126.
5. P. Deuring, An initial-boundary value problem for a certain density-dependent diffusion system, Math. Z. 194 (1987) 375-396.
6. A. Friedman, Partial Differential Equations, Holt, Rinehart and Winston, New York, 1969.
7. J. Uhn Kim, Smooth solutions to a quasi-linear system of diffusion equations for a certain population model, Nonlinear Anal., Theory, Methods & Applications 8 (10) (1984) 1121-1144.
8. Y. Lou, W.-N. Ni, Diffusion, self-diffusion and cross-diffusion, J. Differential Equations 131 (1996) 79-131.
9. Y. Lou, W.-M. Ni, Y. Wu, On the global existence of a cross-diffusion system, Discrete Contin. Dynam. Systems 4 (2) (1998) 193-203.
10. L. Nirenberg, On elliptic partial differential equations, Ann. Scuo. Norm. Sup. Pisa 13 (3) (1959) 115-162.
11. A. Okubo, Diffusion and Ecological Problems: Mathematical Models, Springer, Berlin, New York, 1980.
12. M.H. Protter, H.F. Weinberger, Maximum Principles in Differential Equations, Prentice-Hall Inc, Englewood Cliffs, NJ, 1967.
13. N. Shigesada, K. Kawasaki, E. Teramoto, Spatial segregation of interacting species, J. Theoret. Biol. 79 (1979) 83-99.
14. A. Yagi, Global solution to some quasilinear parabolic system in population dynamics, Nonlinear Anal., Theory, Methods & Applications 21 (8) (1993) 603-630.