Blow-Up and Global Existence for a Degenerate Parabolic System with Nonlocal Sources

This paper investigates the blow‐up and global existence of nonnegative solutions for a class of nonlocal degenerate parabolic system. By using the super‐ and subsolution techniques, the critical exponent of the system is determined. That is, if P c = p 1 q 1 − ( m − p 2 )( n − q 2 ) < 0, then every nonnegative solution is global, whereas if P c > 0, there are solutions that blowup and others that are global according to the size of initial values u 0 ( x ) and v 0 ( x ). When P c = 0, we show that if the domain is sufficiently small, every nonnegative solution is global while if the domain large enough that is, if it contains a sufficiently large ball, there is no global solution.

Abstract licence: CC BY

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