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| The Approach of Solutions for the NonlocalDiffusion Equation to Traveling Fronts |
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| KeyWord:Entire solution Traveling front Nonlocal evolution equation Super-sub |
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| Abstract: |
| The paper is concerned with the asymptotic behavior as t → ±∞
of an entire solution u(x,t) for the nonlocal diffusion equation. With bistable
assumption, it is well known that the model has three different types of travel-
ing fronts. Under certain conditions on the wave speeds, and by some auxiliary
rational functions with certain properties to construct appropriate super- and
sub solutions of the model, we establish two new types of entire solutions
u(x,t) which approach to three travelling fronts or the positive equilibrium as
t → ±∞. |
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