Abstract
This paper is concerned with the behavior of solutions of the Fisher-KPP equation when initial data decay slowly in space. First, we show by a comparison technique that the motion of an interface (or a thin transition layer) can be approximated as a level set of a first-order PDE of Hamilton-Jacobi type. Then by the method of characteristics, it is shown that various (but not all) motion of interfaces can be observed by taking initial data appropriately. Finally, we study the large-time behavior of solutions, especially, the existence of similarly expanding interfaces.
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