Abstract
In this paper, we investigate the positive solution of the nonlocal and degenerate quasilinear parabolic system not in divergence form u t = f ( u ) ( Δ u + a ∫ Ω v d x ) , v t = g ( v ) ( Δ v + b ∫ Ω u d x ) with null Dirichlet boundary conditions. The blow-up and global existence criteria are obtained. Furthermore, we prove that under certain conditions the solutions have global blow-up.
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