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Convergence to spatial-temporal clines in the Fisher equation with time-periodic fitnesses

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Abstract

The asymptotic behavior as t → ∞ of the solutions with values in the interval (0, 1) of a reaction-diffusion equation of the form

$$\left\{ \begin{gathered}\frac{{\partial u}}{{\partial t}} - \Delta u = m(x,t,u)u(1 - u) in \Omega \times (0,\infty ) \hfill \\\frac{{\partial u}}{{\partial n}} = 0 on \partial \Omega \times (0,\infty ) \hfill \\\end{gathered} \right.$$

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Authors and Affiliations

  1. Mathematisches Institut, Universität Zürich, Rämistrasse 74, CH-8001, Zürich, Switzerland

    P. Hess

  2. School of Mathematics, University of Minnesota, 206 Church Street, 55455, Minneapolis, MN, USA

    H. Weinberger

Authors
  1. P. Hess
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  2. H. Weinberger
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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

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