| Abstract: |
| In this talk I will present the recent study on a free boundary problem of the nonlinear diffusion equations
$u_t=u_{xx}+f(u)$, $t\in (0, \infty)$, $x\in (ct, h(t))$. The nonlinearity $f$ is $C^1$ function satisfying $f(0)=0$, $c>0$ is a given constant, that is $c=ct$ is a given forced moving boundary and $h(t)$ is a free boundary which is determined by a Stefan-like condition. At left boundary $x=ct$, zero Dirichlet boundary condition is imposed. When $f$ is logistic nonlinearity, [Matsuzawa, to appear, arXiv:1708.01995] dealt with this problem. In this talk I will present the extension of the earlier study to much more general nonlinear functions $f$. I will also give the The approach here is quite different from that used in my previous work. |
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