Existence of traveling wave solutions for a nonlocal bistable equation: an abstract approach

Details Existence of traveling wave solutions for a nonlocal bistable equation: an abstract approach Existence of traveling wave solutions for a nonlocal bistable equation: an abstract approach

2008-10-19

arxiv.org/abs/0810.3398v1

Mathematics

Analysis of PDEs

27 pages, submitted to Publications of the Research Institute for Mathematical Sciences

Scientific paper

We consider traveling fronts to the nonlocal bistable equation. We do not
assume that the Borel-measure is absolutely continuous with respect to the
Lebesgue measure. We show that there is a traveling wave solution with monotone
profile. In order to prove this result, we would develop a recursive method for
abstract monotone dynamical systems and apply it to the equation.

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