Abstract
The asymptotic behavior as t → ∞ of the solutions with values in the interval (0, 1) of a reaction-diffusion equation of the form
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Alikakos, N. D., Hess, P., Matano, H: Discrete order-preserving semigroups and stability for periodic parabolic differential equations. J. Differ. Equations (in press)
Beltramo, A., Hess, P.: On the principal eigenvalue of a periodic-parabolic operator. Commun. Partial. Differ. Equations 9, 919–941 (1987)
Conley, C.: An application of Wazewski's method to a nonlinear boundary value problem which arises in population genetics. J. Math. Biol. 2, 241–249 (1975)
Dancer, E. N., Hess, P.: On stable solutions of quasilinear periodic-parabolic problems. Ann. Sc. Norm. Pisa 14, 123–141 (1987)
Fife, P. C., Peletier, L. A.: Nonlinear diffusion in population genetics. Arch. Rat. Mech. Anal. 64, 93–109 (1977)
Fisher, R. A.: The wave of advance of an advantageous gene. Ann. Eugen. 7, 355–369 (1937)
Fisher, R. A.: Gene frequencies in a cline determined by selection and diffusion. Biometrics 6, 353–361 (1950)
Fleming, W. H.: A selection-migration model in population genetics. J. Math. Biol. 2, 219–234 (1975)
Friedman, A.: Partial differential equations of parabolic type. Englewood Cliffs, NJ: Prentice-Hall 1964
Haldane, J. S.: The theory of a cline. J. Genetics 48, 277–284 (1948)
Henry, D.: Geometric theory of partial differential equations (Lect. Notes Math., vol. 840) Berlin Heidelberg New York: Springer 1981
Hess, P.: Spatial homogeneity of stable solutions of some periodic-parabolic problems with Neumann boundary conditions. J. Differ. Equations 68, 320–331 (1987)
Nagylacki, T.: Conditions for the existence of clines. Genetics 80, 595–615 (1975)
Protter, M. H., Weinberger, H. F.: Maximum principles in differential equations. Berlin Heidelberg New York: Springer 1984
Slatkin, M.: Gene flow and selection in a cline. Genetics 75, 733–756 (1973)
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Hess, P., Weinberger, H. Convergence to spatial-temporal clines in the Fisher equation with time-periodic fitnesses. J. Math. Biol. 28, 83–98 (1990). https://doi.org/10.1007/BF00171520
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DOI: https://doi.org/10.1007/BF00171520