| Abstract: |
| In this talk, I will discuss the long-time dynamical behavior of solutions to a nonlinear Stefan problem for a reaction diffusion equation.
I will show that when the nonlinearity is a positive bistable type nonlinearity which is a certain kind of multi-stable type nonlinearity, the asymptotic behavior of the solutions is classified into four cases: vanishing, small spreading, big spreading, and transition.
In particular, I will show that when the transition occurs, the solution converges to an equilibrium solution which is radially symmetric and radially decreasing and centered at some point as time goes to infinity locally uniformly. |
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