Blow-Up and Global Existence for a Degenerate Parabolic System with Nonlocal Sources. (21st May 2012)

• Record Type: Journal Article
• Authors: Zhengqiu, Ling; Zejia, Wang
• Other Names: Rogovchenko Yuriy Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2012(2012)
• Publication Date: 2012-05-21
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2012/956564
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : 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.