| Abstract: |
| In this talk, I will present a recent result on a free boundary problem for a multi-stable reaction diffusion equations 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 one dimensional problem, under certain condition, a solution approaches to so-called propagating terrace which consists of a semi-wave and a traveling wave. In this talk, I will present that for higher dimensional case, under certain condition, a solution approaches to the radial propagating terrace. In particular, this radial propagating terrace has two kinds of logarithmic shiftings which come from free boundary problem and
Cauchy problem, respectively. |
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