Blow-up and Global Existence for a Nonlocal Degenerate Parabolic System
Acta mathematica scientia,Series A
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Chen Yujuan
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Abstract: This paper investigates the blow-up and global existence of nonnegative solutions for a class of nonlocal degenerate parabolic system. The sub and super solutions method and the regularization skill are used. The critical exponent of the system is gained. It's proved that if pc=(p1+p2)(q1+q2)- mn, every nonnegative solution is global, whereas if pc>0, there exists both global and blow-up nonnegative solution. When pc=0, we show that if the domain is sufficiently small, every nonnegative solution is global while if the domain is large enough that is, if it contains a sufficiently large ball, there is no global solution. The related results of papers [8,10,11] are the special cases of this paper.
Key words: Degenerate parabolic system, Nonlocal source, Blow-up
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Chen Yujuan.
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http://121.43.60.238/sxwlxbA/EN/Y2006/V26/I5/731
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