| Abstract: |
| This talk is concerned with a free boundary problem which consists of a reaction-diffusion equation in a one-dimensional interval and a free boundary condition of Stefan type at one of boundary points of the interval. We put Neumann or Dirichlet condition at the other boundary point. When the reaction term is given by a certain class of bistable function, such a free boundary problem exhibits different types of spreading behaviors with free boundaries going to infinity as time tends to infinity. Asymptotic spreading speeds of free boundaries are different or same depending on nonlinear function. We will study the structure of spreading solutions and derive precise asymptotic estimates on their profiles. |
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