Persistence for a class of triangular cross diffusion parabolic systems

Advanced Nonlinear Studies

Volumn 5, Issue 4, 2005, Pages 493-514

  Le, Dung ^a   Nguyen, Toan Trong ^a  

^a UNIVERSITY OF TEXAS AT SAN ANTONIO   (United States)

Author keywords

Cross diffusion system; Global attractor; Uniform persistence

Indexed keywords

EID: 29144461972     PISSN: 15361365     EISSN: None     Source Type: Journal    
DOI: 10.1515/ans-2005-0403     Document Type: Article

References (21)

1. H. Amann, Dynamic theory of quasilinear parabolic systems-III, global existence, Math. Z. 202 (1989), pp. 219-250.
2. R. S. Cantrell and C. Cosner, Diffusive logistic equations with indefinite weights: population models in disrupted environments. II, SLAM J. Math. Anal. 22, no. 4, (1991), pp. 1043-1064.
3. R. S. Cantrell and C. Cosner, Conditional persistence in logistic, models via nonlinear diffusion, Proc. Roy. Soc. Edinburgh. 132A (2002), pp. 267-281.
4. 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 10 (2004), pp. 719-730.
5. G. Cupini and R. Petti, Morrey spaces and local regularity of minimizers of variational integrals, Rend. Mat. Appl. 21 (2001), no. 1-4, pp. 121-141.
6. A. Friedman, Partial differential equations, Holt, Rinehart and Winston, New York, 1969.
7. J. Hale. Asymptotic Behavior of Dissipative Systems, American Math. Soc. Math. Surveys and Monographs 25, 1988.
8. G. Hetzer and W. Shen, Uniform persistence, coexistence, and extinction in almost periodic/nonautonomous competition diffusion system, SIAM J. Math. Anal. 34, no. 1,(2002), pp. 204-227.
9. M. W. Hirsch, H. L. Smith, and X-Q. Zhao, Chain transitivity, attractivity, and strong repellors for semidynamical systems, J. Dyn. Diff. Eq. 13, no. 1, (2001), pp. 107-131.
10. K. Kuto, Stability of steady-state solutions to a preypredator system with cross-diffusion, J. Diff. Eqn. 197 (2004), pp. 293-314.
11. O.A. Ladyzenskaja, V. A. Solonnikov, and N. N. Ural'tseva, Linear and Quasilinear Equations of Parabolic type, AMS Transl. Monographs, vol. 23, 1968.
12. D. Le, Hölder regularity for certain strongly coupled parabolic systems, J. Diff. Eq. 151(1999), no. 2, pp. 313-344.
13. D. Le, Cross diffusion systems on n spatial dimensional domains, Indiana Univ. Math. J. 51, no. 3, (2002), pp. 625-643.
14. D. Le, Dynamics of a bio-reactor model with chemotaxis, J. Math. Anal. App. 257 (2002), pp. 188-207.
15. D. Le, Global existence for a class of strongly coupled parabolic systems, to appear on Annali di Matematica Pura ed Applicata.
16. D. Le and T. Nguyen, Global existence for a class of triangular parabolic systems on domains of arbitrary dimension, Proc. Amer. Math. Soc. 133, no. 7,(2005), pp. 1985-1992
17. D. Le and T. Nguyen, Uniform boundedness of solutions for triangular parabolic system, submitted.
18. D. Le and T. Nguyen, Strong positivity of solutions to parabolic equations on nonsmooth domains, submitted.
19. D. Le, L. Nguyen and T. Nguyen, Shigesada-Kawasaki-Teramoto Model on Higher Dimensional Domains, EJDE 72 (2003), pp. 1-12.
20. D. Palagachev, M. Ragusa, and L. Softova, Regular oblique derivative problem in Morrey spaces, EJDE 39 (2000), pp. 1-17.
21. N. Shigesada, K. Kawasaki, E. Teramoto, Spatial segregation of interacting species, J. Theor. Biol. 79 (1979), pp. 83-99.