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Global existence and blow‐up solution for doubly degenerate parabolic system with nonlocal sources and inner absorptions
Author(s) -
Wu Xiulan,
Gao Wenjie
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2813
Subject(s) - degenerate energy levels , mathematics , bounded function , domain (mathematical analysis) , dirichlet boundary condition , boundary (topology) , mathematical analysis
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.