title: Convergence to spatial-temporal clines in the Fisher equation with time-periodic fitnesses.
abstract: The asymptotic behavior as t----infinity of the solutions with values in the interval (0, 1) of a reaction-diffusion equation of the form (Formula: see text) is studied. Conditions on m which are satisfied when m is nonincreasing in mu and which imply that every solution converges to some periodic limit function are found. Except in some very special and well-defined circumstances, the limit is the same for all solutions, so that it is a global attractor. This global attractor may be one of the trivial solutions 0 or 1, or it may be a spatial-temporal cline. The linear stability properties of the trivial states serve to distinguish between these cases.
authors.affiliation: Mathematisches Institut, Universität Zürich, Switzerland.
authors.forename: P
authors.initials: P
authors.lastname: Hess
authors.forename: H
authors.initials: H
authors.lastname: Weinberger
mesh_terms: D008433:Mathematics; D008954:Models, Biological; D015233:Models, Statistical; D013997:Time Factors