Article

Journal of Dynamics and Differential Equations

, Volume 19, Issue 4, pp 895-914

First online:

Irregular Behavior of Solutions for Fisher’s Equation

  • Eiji YanagidaAffiliated withMathematical Institute, Tohoku University Email author 

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This paper is concerned with the irregular behavior of solutions for Fisher’s equation when initial data do not decay in a regular way at the spatial infinity. In the one-dimensional case, we show the existence of a solution whose profile and average speed are not convergent. In the higher-dimensional case, we show the existence of expanding fronts with arbitrarily prescribed profiles. We also show the existence of irregularly expanding fronts whose profile varies in time. Proofs are based on some estimate of the difference of two distinct solutions and a comparison technique.

Keywords

Fisher’s equation irregular behavior expanding front

Mathematics Subject Classification

35B99 35K15 35K57