Abstract
In this paper we study a localized nonlinear diffusion equation u t = Δ u m + λ 1 u p + λ 2 u q ( 0 , t ) subject to null Dirichlet boundary condition with p , q ≥ 0 , max { p , q } > m > 1 , and λ 1 , λ 2 > 0 . We investigate interactions among the localized and local sources, nonlinear diffusion with the zero boundary value condition to establish blow-up rates and uniform blow-up profiles of solutions under different dominations. In addition, as results of the interactions of multiple nonlinearities, the blow-up sets of solutions, namely, total versus single point blow-up of solutions are also determined.
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