| Abstract: |
| In this talk, I will present a recent result on a free boundary problem for a multi-stable reaction-diffusion equation of the form $u_t=\Delta u+f(u)$ with a radially symmetric setting in high space dimensions. In particular, I will focus on positive bistable nonlinearity $f$ introduced by [Kawai-Yamada, 2016]. Recently [Kaneko-Matsuzawa-Yamada, 2020] revealed that for the one-dimensional problem, under certain conditions, a solution approaches a so-called propagating terrace that consists of a semi-wave and a traveling wave.
In this talk, I will present that for higher dimensional case, under certain conditions, the solution generates a propagating terrace with logarithmic shiftings. In particular, I will show that the solution has two kinds of logarithmic shifting which come from the free boundary problem and Cauchy problem, respectively. |
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