×
Brown, K. J.

Spatially inhomogeneous steady state solutions for systems of equations describing interacting populations. (English) Zbl 0518.92017

J. Math. Anal. Appl. 95, 251-264 (1983).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0518.92017

Cited in 1 Review
Cited in 11 Documents

MSC:

92D25 Population dynamics (general)
35B32 Bifurcations in context of PDEs
35J25 Boundary value problems for second-order elliptic equations

Keywords:

interacting populations; Dirichlet boundary conditions; reaction- diffusion system; steady states; decoupling technique; predator-prey systems; competing populations; co-operating populations
PDF BibTeX XML Cite
\textit{K. J. Brown}, J. Math. Anal. Appl. 95, 251--264 (1983; Zbl 0518.92017)
Full Text: DOI

References:

[1] Amann, H., Invariant sets and existence theorems for semilinear parabolic and elliptic systems, J. Math. Anal. Appl., 65, 432-467 (1978) · Zbl 0387.35038
[2] Amann, H., Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, SIAM Rev., 18, 620-709 (1976) · Zbl 0345.47044
[3] Auchmuty, J. F.G; Nicolis, G., Bifurcation analysis of nonlinear reaction-diffusion equations, I, Bull. Math. Biol., 37, 1-43 (1975) · Zbl 0357.35048
[4] Catalano, G.; Eilbeck, J. C.; Monroy, A.; Parisi, E., A numerical study of a system of nonlinear parabolic equations with solutions simulating the development of biological patterns, Phys. D, 3, 439-456 (1981) · Zbl 1194.37172
[5] Crandall, M. G.; Rabinowitz, P. H., Bifurcation from simple eigenvalues, J. Funct. Anal., 8, 321-340 (1971) · Zbl 0219.46015
[6] Hadeler, K. P.; Rothe, F.; Vogt, H., Stationary solutions of reaction-diffusion equations, Math. Methods in Appl. Sci., 1, 418-431 (1979) · Zbl 0424.35047
[7] Herschkowitz-Kaufman, M., Bifurcation analysis of nonlinear reaction diffusion equations. II. Steady state solutions and comparison with numerical simulations, Bull. Math. Biol., 37, 589-635 (1975) · Zbl 0324.92004
[8] Leung, A.; Clark, D., Bifurcations and large time asymptotic behaviour for prey-predator reaction-diffusion equations with Dirichlet boundary data, J. Differential Equations, 35, 113-127 (1980) · Zbl 0427.35014
[9] Pao, C. V., Coexistence stability of a competition-diffusion system in population dynamics, J. Math. Anal. Appl., 83, 54-76 (1981) · Zbl 0479.92013
[10] Rabinowitz, P. H., Some global results for nonlinear eigenvalue problems, J. Funct. Anal., 7, 487-513 (1971) · Zbl 0212.16504
[11] Rothe, F., Some analytic results about a simple reaction-diffusion system for morphogenesis, J. Math. Biol., 7, 375-384 (1979)
[12] Tsai, L. Y., Nonlinear boundary value problems for systems of second order elliptic differential equations, Bull. Inst. Math. Acad. Sinica, 5, 157-165 (1977) · Zbl 0356.35029
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.