| Abstract: |
| In this talk, we will investigate the longtime behavior of solutions to a temporally discrete diffusion equation with a fixed boundary and a free boundary respectively in one space dimension. Such equation can be equivalent to an integrodifference equation, another important time discrete equation that provides powerful tools for the study of dispersal phenomena. We first discuss the global dynamics of the equation in a fixed bounded domain. With a Stefan type free boundary, we then give a new well-posedness proof and the regular spreading-vanishing dichotomy for the corresponding problem. Moreover, a modified comparison principle for the time discrete free boundary problem is proved in an effort to provide the sufficient conditions for dichotomy. It is the first attempt to study the temporally discrete diffusive phenomenon with a free boundary. |
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