Global existence and blow‐up solution for doubly degenerate parabolic system with nonlocal sources and inner absorptions

This paper deals with the following doubly degenerate parabolic systemu t − div | ∇ u m| p − 2 ∇ u m= ∫ Ωvr 1d x − α us 1, x ∈ Ω , t > 0 ,v t − div | ∇ v n| q − 2 ∇ v n= ∫ Ωur 2d x − β vs 2, x ∈ Ω , t > 0 , with null Dirichlet boundary conditions in a smooth bounded domain Ω ⊂  R N , where m , n  ≥ 1, p ,  q  ≥ 2, r 1 , r 2 , s 1 , s 2  ≥ 1, α , β  < 0. Under appropriate hypotheses, we prove that the solution either exists globally or blows up in finite time. Copyright © 2013 John Wiley & Sons, Ltd.