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Journal of Function Spaces and Applications
Volume 2012 (2012), Article ID 530861, 15 pages
http://dx.doi.org/10.1155/2012/530861
Research Article

Global Nonexistence of Solutions for Viscoelastic Wave Equations of Kirchhoff Type with High Energy

College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China

Received 12 February 2012; Accepted 26 March 2012

Academic Editor: Amol Sasane

Copyright © 2012 Gang Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider viscoelastic wave equations of the Kirchhoff type utt-M(u22)Δu+0tg(t-s)Δu(s)ds+ut=|u|p-1u with Dirichlet boundary conditions, where p denotes the norm in the Lebesgue space Lp. Under some suitable assumptions on g and the initial data, we establish a global nonexistence result for certain solutions with arbitrarily high energy, in the sense that limtT*-(u(t)22+0tu(s)22ds)= for some 0<T*<+.