General Decay and Blow-Up of Solutions for a System of Viscoelastic Equations of Kirchhoff Type with Strong Damping. (4th February 2014)

• Record Type: Journal Article
• Authors: Liu, Wenjun; Li, Gang; Hong, Linghui
• Other Names: Ziemer William Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2014(2014)
• Publication Date: 2014-02-04
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2014/284809
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : The general decay and blow-up of solutions for a system of viscoelastic equations of Kirchhoff type with strong damping is considered. We first establish two blow-up results: one is for certain solutions with nonpositive initial energy as well as positive initial energy by exploiting the convexity technique, the other is for certain solutions with arbitrarily positive initial energy based on the method of Li and Tsai. Then, we give a decay result of global solutions by the perturbed energy method under a weaker assumption on the relaxation functions.