| Abstract: |
| We consider a free boundary problem arising from segregation of two species with high competition. One species moves according to the classical diffusion and the other adopts a nonlocal diffusion strategy. Being a fully nonlinear nonlocal model, it is challenging to design effective ways to compute the solution, especially to capture the free boundary well. We propose an iterative scheme that constructs a sequence of monotone viscosity supersolutions that is shown to converge to the viscosity solution (in the sense of Crandall-Lions). The numerical method applies to general domains in all dimensions. Moreover, for simple domains it can be shown that the sequence of supersolutions converges with a precise rate. We will shown numerical experiments in the end. This is a joint work Luis Caffarelli and Irene Gamba. |
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