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Global existence and blow-up of solutions in reaction-diffusion system with free boundary. (English) Zbl 1449.35025

Summary: This paper is concerned with a free boundary problem for the reaction-diffusion system with coupled nonlinear reaction terms. For simplicity, we assume that the conditions and solutions are radially symmetric. At first, we give the local existence and uniqueness of the positive solution. Then, we consider the blow-up property and the long time behavior of the solution. When \({m_2} - {m_1} > -1, {n_1} - {n_2} > -1\), the solution blows up if the initial value is large enough.

MSC:

35B09 Positive solutions to PDEs
35B44 Blow-up in context of PDEs
35K57 Reaction-diffusion equations
35R35 Free boundary problems for PDEs
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