| Abstract: |
| In this talk, we study a time-fractional Fisher-KPP type equation in which the time derivative is given by the Caputo derivative. The main focus is on the long-time behavior of front solutions. After briefly reviewing the background of the equation, we present numerical results and discuss the qualitative properties of the solutions. It is known that this equation does not admit classical traveling wave solutions. To describe the long-time behavior, we assume that the solution asymptotically behaves like a traveling wave solution and analyze possible wave profiles to which the solution may converge. Based on this analysis, we construct traveling wave-like solutions that describe the asymptotic behavior of the front solution. |
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