Invariant regions for quasilinear reaction-diffusion systems and applications to a two population model

Nonlinear Differential Equations and Applications

Volumn 3, Issue 4, 1996, Pages 421-444

  Küfner, Konrad Horst Wilhelm ^a  

^a UNIVERSITY OF BAYREUTH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0009035974     PISSN: 10219722     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01193829     Document Type: Article

References (22)

1. H. AMANN, Dynamic Theory of Quasilinear Parabolic Equations, I. Abstract Evolution Equations, Nonlinear Anal., Theory Methods Appl. 12, 895-919 (1988)
2. H. AMANN, Dynamic Theory of Quasilinear Parabolic Equations, II. Reaction-Diffusion Systems, Differ. Integral Equations 3, 13-75 (1990)
3. H. AMANN, Dynamic Theory of Quasilinear Parabolic Equations, III. Global Existence, Math. Z. 202, 219-250 (1989)
4. H. AMANN, Quasilinear Evolution Equations and Parabolic Systems, Trans. Amer. Math. Soc. 293, 191-227 (1986)
5. H. AMANN, Global Existence for Semilinear Parabolic Systems, J. Reine Angew. Math. 360, 47-83 (1985)
6. H. AMANN, Existence and Regularity for Semilinear Parabolic Evolution Equations, Annali Scuola Norm. Pisa Cl. Sci. (4) 11, 593-676 (1984)
7. H. AMANN, Global Existence and Positivity for Triangular Quasilinear Reaction-Diffusion Systems, Unpublished Manuscript (1989)
8. K.N. CHUEH, C.C. CONLEY, J.A. SMOLLER, Positively Invariant Regions for Systems of Nonlinear Diffusion Equations, Indi. Univ. Math. J. 26, 373-392 (1977)
9. P. DEURING, An Initial-Boundary-Value Problem for a Certain Density-Dependent Diffusion System, Math. Z. 194, 375-396 (1987)
10. J.U. KIM, Smooth Solutions to a Quasilinear System of Diffusion Equations for a Certain Population Model, Nonlinear Anal., Theory Methods Appl. 8, 1121-1144 (1984)
11. K.H.W. KÜFNER, Maximumprinzip, Invariante Gebiete und A Priori Schranken für Parabolische Gleichungen, Diploma Thesis, Bayreuth (1990)
12. K.H.W. KÜFNER, Invariante Gebiete für stark gekoppelte quasilineare parabolische Systeme in Divergenzform und globale Existenz für ein spezielles Gleichungssystem aus der Populationsdynamik, PhD Thesis, Bayreuth (1994)
13. M. MIMURA, Stationary Pattern of Some Density-Dependent Diffusion System with Competitive Dynamics, Hiroshima Math. J. 11, 621-635 (1981)
14. M.A. POZIO, A. TESEI, Global Existence of Solutions for a Strongly Coupled Quasilinear Parabolic System, Nonlinear Anal., Theory Methods Appl. 14, 657-689 (1990)
15. M.H. PROTTER, H.F. WEINBERGER, Maximum Principles in Differential Equations. Springer Verlag, New York (1984). (First published in Prentice Hall, Englewood Cliffs, New Jersey (1967))
16. R. REDHEFFER, W. WALTER, Invariant Sets for Systems of Partial Differential Equations, I. Parabolic Equations. Arch. Rat. Mech. Anal. 67, 41-52 (1977)
17. R. REDLINGER, Invariant Sets for Strongly Coupled Reaction-Diffusions Systems under General Boundary Conditions, Arch. Rat. Mech. Anal. 108, 281-291 (1989)
18. B.J. SCHMITT, Personal Communication.
19. N. SHIGESADA, K. KAWASAKI, E. TERAMOTO, Spatial Segregation of Interacting Species, J. Theor. Biol. 79, 83-99 (1979)
20. M. WIEGNER, Global Solutions to a Class of Strongly Coupled Parabolic Systems, Math. Ann. 292, 711-727 (1992)
21. A. YAGI, Global Solutions to some Quasilinear Parabolic Systems in Population Dynamics, Nonlinear Anal., Theory Methods Appl. 21, 603-630 (1993)
22. Y. YAMADA, Global Solutions for Quasilinear Parabolic Systems with Cross-Diffusion Effects, Preprint