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.
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Dedicated to Professor Pavol Brunovsky on his 70th birthday.
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Yanagida, E. Irregular Behavior of Solutions for Fisher’s Equation. J Dyn Diff Equat 19, 895–914 (2007). https://doi.org/10.1007/s10884-007-9096-8
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DOI: https://doi.org/10.1007/s10884-007-9096-8