Global existence and blow-up of solutions for a system of Petrovsky equations. Issue 16 (10th December 2017)

• Record Type: Journal Article
• Authors: Ye, Yaojun
• Is Part Of: Applicable analysis. Volume 96:Issue 16(2017)
• Page Start: 2869
• Page End: 2890
• Publication Date: 2017-12-10
• Subjects: Global existence -- exponential decay estimates -- blow-up -- Petrovsky systems; 35L75 -- 35B40 -- 35L20; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2016.1249862
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : The initial-boundary value problem for a system of Petrovsky equations with memory and nonlinear source terms in bounded domain is studied. The existence of global solutions for this problem is proved by constructing a stable set, and obtain the exponential decay estimate of global solutions. Meanwhile, under suitable conditions on relaxation functions and the positive initial energy as well as non-positive initial energy, it is proved that the solutions blow up in the finite time and the lifespan estimates of solutions are also given.