| Abstract: |
| This talk is devoted to the problem how the tail of the nonlocal dispersal kernel influences the propagation speed of the Fisher-KPP equation in time periodic environment. When the nonlocal dispersal kernel is exponentially bounded, applying the monotone dynamical system theory, we prove that the solution level set is asymptotically linear in time. When the nonlocal dispersal kernel is exponentially unbounded, the solution level set propagates with an infinite asymptotic speed. Further, based on a heaviness characterization for the kernel tail, we establish the fine estimates of the fundamental solution and then determine sharp bounds for the solution level set by constructing subtle upper and lower solutions. The bounds are expressed in terms of the decay of the nonlocal dispersal kernel. |
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