| Abstract: |
| In this talk, I will present recent results about a free boundary problems for a reaction diffusion equations of the form $u_t=\Delta u+f(u)$
with multi-stable type nonlinearity $f$. In particular, I will focus on the problem with a radially symmetric setting in
high space dimensions. I will first give a result about classification of asymptotic behaviors of the unique solution to
the free boundary problem. For the classification we will see that it is important to study the solution set for corresponding stationary problem and some classical results for some elliptic problems are useful to investigate the stationary problem. I will also present some results about the asymptotic spreading speed of the free boundary and the asymptotic profile of the solutions. |
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