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| We discuss free boundary problems for reaction-diffusion equations in multi-dimensions, where unknown functions are the population density of invasive or new species and the spreading front of the species which is represented as a free boundary. Such a model was first proposed by Du-Lin (2010) in one dimension and a multi-dimensional case was studied by Du-Guo (2012). We consider both radially and non-radially symmetric solutions for the free boundary problems which admit exterior domains. I will present some results on the unique existence of solutions and asymptotic behaviors of solutions as $t\to\infty$. |
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