Extinction behavior of solutions for a quasilinear parabolic system with nonlocal sources

This paper deals with the extinction properties of solutions for a quasilinear parabolic system u t = div ( | ? u | p - 2 ? u ) + ? ? v α ( x , t ) dx , v t = div ( | ? v | q - 2 ? v ) + ? ? u β ( x , t ) dx with zero Dirichlet boundary conditions in a smooth bounded domain ? ? R N ( N ? 1 ) , where 1 < p , q < 2 and α , β 0 . By using the comparison principle and energy estimate methods, we obtain the sufficient conditions of extinction solutions.

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