| Abstract: |
| In this talk, we consider the Cauchy problem for an anisotropic reaction-diffusion equation with a multi-stable nonlinearity on $\mathbb{R}^N$ and study the asymptotic behavior of its solutions. Matano, Mori, and Nara (2019) previously investigated this problem with a bistable nonlinearity, demonstrating that, under suitable conditions on the initial function, the solution develops a spreading front closely approximated by the expanding Wulff shape for sufficiently large times. In this talk, we extend their results to cases involving multi-stable nonlinearities, where the nonlinearity can be decomposed into multiple bistable components. |
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