关键词: 退化方程组, 非局部源, 爆破

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 p_c=(p₁+p₂)(q₁+q₂)- mn, every nonnegative solution is global, whereas if p_c>0, there exists both global and blow-up nonnegative solution. When p_c=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