Quasisolutions and global attractor of reaction-diffusion systems

Nonlinear Analysis, Theory, Methods and Applications

Volumn 26, Issue 12, 1996, Pages 1889-1903

  Pao, C V ^a  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

Author keywords

Assymptotic behavior; Coexistence and persistence; Global attractor; Quasisolution; Reaction diffusion

Indexed keywords

ASYMPTOTIC STABILITY; BOUNDARY CONDITIONS; CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; DYNAMICS; FUNCTIONS; ITERATIVE METHODS; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; MAXIMUM PRINCIPLE;

ACTIVATOR INHIBITOR SYSTEM; COEXISTENCE AND PERSISTENCE; COUPLED PARABOLIC SYSTEM; ELLIPTIC SYSTEM; GLOBAL ATTRACTOR; LINEAR SCALAR PROBLEMS; QUASISOLUTIONS; REACTION DIFFUSION SYSTEMS; VOLTERRA-LOTKA COMPETITION MODEL;

BOUNDARY VALUE PROBLEMS;

EID: 0030174199     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/0362-546X(95)00058-4     Document Type: Article

References (25)

1. BROWN P. N., Decay to uniform states in ecological interactions, SIAM J. appl. Math. 38, 22-37 (1980).
2. CASTEN R. G. & HOLLAND C. J., Stability properties of solutions to systems of reaction-diffusion equations, J. diff. Eqns 27, 266-273 (1978).
3. CONWAY E. D., HOFF D. & SMOLLER S. A., Large time behavior of solutions of systems of nonlinear reaction-diffusion equations, SIAM J. math. Analysis 35, 1-16 (1978).
4. FENG W., Coupled system of reaction-diffusion equations and application to carrier facilitated diffusion, Nonlinear Analysis 17, 285-311 (1991).
5. FENG W. & RUAN W. H., Coexistence and stability in a three-species competition model, preprint.
6. FIFE P. C. & TANG M. M., Comparison principles for reaction-diffusion systems, J. diff. Eqns 40, 168-185 (1981).
7. GARDNER R. A., Comparison and stability theorems for reaction-diffusion systems, J. diff. Eqns 37, 60-69 (1980).
8. LAKSHMIKANTHAM V. & VATSALA A. S., Stability results for solutions of reaction-diffusion equations by the method of quasisolutions, Applic. Analysis 12, 229-235 (1981).
9. LEUNG A. W. & CLARK D., Bifurcation and large time asymptotic behavior for prey-predator reaction-diffusion equations with Dirichlet boundary data, J. diff. Eqns 25, 113-127 (1980).
10. PAO C. V., Nonlinear Parabolic and Elliptic Equations. Plenum Press, New York (1992).
11. PAO C. V., On nonlinear reaction-diffusion equations, J. math. Analysis applic. 87, 165-198 (1982).
12. RUAN W. H., Bounded solutions for reaction-diffusion systems with nonlinear boundary conditions, Nonlinear Analysis 169, 157-178 (1992).
13. SATTINGER D. H., Monotone methods in nonlinear elliptic and parabolic boundary-value problems, Indiana Univ. math. J. 21, 979-1000 (1972).
14. ZHOU L. & PAO C. V., Asymptotic behavior of a competition-diffusion system in population dynamics, Nonlinear Analysis 6, 1163-1184 (1982).
15. BROWN K. J., Spatially inhomogeneous steady-state solutions for systems of equations describing interacting populations, J. math. Analysis Applic 95, 251-264 (1983).
16. FREEDMAN H. I. & WALTMAN P., Persistence in a model of three competitive populations, Math. Biosci. 73, 89-101 (1985).
17. HALLMAN T. G., SVOBODA L. J. & GARD T. C., Persistence and extinction in the three species Lotka-Volterra competitive systems. Math Biosci. 46, 117-124 (1979).
18. KORMAN P. & LEUNG A., On the existence and uniqueness of positive steady-states in the Volterra-Lotka ecological models with diffusion, Applic. Analysis 26, 145-160 (1987).
19. LU X., Persistence and extinction in a competition-diffusion system with time delays, Can. appl. Math. Quart. 2, 231-246 (1994).
20. LADDE G. S., LAKSHMIKANTHAM V. & VATSALA A. S., Monotone Iterative Techniques for Nonlinear Differential Equations. Pittman, Boston (1985).
21. ALI S. W. & COSNER C., On the uniqueness of the positive steady-state Lotka-Volterra models with diffusion, J. math. Analysis applic. 163, 329-341 (1992).
22. VARGA R. S., Matrix Iterative Analysis. Prentice Hall, Englewood, NJ (1962).
23. BLAT J. & BROWN K. J., Global bifurcation of positive solutions in some systems of elliptic equations, SIAM J. math. Analysis 17, 1339-1353 (1986).
24. GIERER A., Generation of biological patterns and form: Some physical, mathematical, and logical aspects, Prog. Biophys. Molec. Biol. 37, 1-47 (1981).
25. MEINHARDT H., Models of Biological Pattern Formulation. Academic Press, New York (1982).