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

@article{Hess1990ConvergenceTS,
  title={Convergence to spatial-temporal clines in the Fisher equation with time-periodic fitnesses.},
  author={Peter Otto Hess and Hans Weinberger},
  journal={Journal of mathematical biology},
  year={1990},
  volume={28 1},
  pages={83-98}
}
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… CONTINUE READING