Abstract
This paper deals with a class of porous medium systems with moving localized sources u t = u r 1 ( Δ u + a f ( v ( x 0 ( t ) , t ) ) ) , v t = v r 2 ( Δ v + b g ( u ( x 0 ( t ) , t ) ) ) with homogeneous Dirichlet boundary conditions. It is shown that under certain conditions, solutions of the above system blow up in finite time for large a and b or large initial data while there exist global positive solutions to the above system for small a and b or small initial data. Moreover, in the one dimensional space case, it is also shown that all global positive solutions of the above problem are uniformly bounded.
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