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

Abstract EN

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 Pc=p1q1−(m−p2)(n−q2)<0, then every nonnegative solution is global, whereas if Pc>0, there are solutions that blowup and others that are global according to the size of initial values u0(x) and v0(x).

When Pc=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.