Critical blowup exponents for a system of reaction-diffusion equations with absorption
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- Bedjaoui, N. & Souplet, P. Z. angew. Math. Phys. (2002) 53: 197. doi:10.1007/s00033-002-8152-9
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We consider a system of two reaction-diffusion equations with absorption, under Dirichlet boundary conditions, modelling the cooperative interaction of two diffusing biological species. We obtain optimal conditions on the exponents of the reaction and absorption terms for the existence of blowing up solutions, or for the global existence and boundedness of all solutions. The proofs of blowup rely on comparison with carefully constructed self-similar weak subsolutions with compact support.