Abstract
This paper deals with localized parabolic equations u t = Δ u + u m ( x 0 , t ) e p v ( x 0 , t ) , v t = Δ v + u q ( x 0 , t ) e n v ( x 0 , t ) with homogeneous Dirichlet boundary conditions, where x 0 is any fixed point in a bounded domain of R N . The optimal classification of non-simultaneous and simultaneous blow-up phenomena is proposed for all of the nonnegative exponents. Moreover, uniform blow-up profiles are obtained for all kinds of simultaneous blow-up solutions.
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