Existence and Asymptotic Behavior of Global Solutions for a Class of Nonlinear Higher-Order Wave Equation. (22nd February 2010)

• Record Type: Journal Article
• Authors: Ye, Yaojun
• Other Names: García-Huidobro Marta Academic Editor.
• Is Part Of: Journal of inequalities and applications. Volume 2010(2010)
• Publication Date: 2010-02-22
• Subjects: Inequalities (Mathematics) -- Periodicals; 512.97
• DOI: 10.1155/2010/394859
• Languages: English
• ISSNs: 1029-242X

Abstract

Abstract : The initial boundary value problem for a class of nonlinear higher-order wave equation with damping and source termu t t + A u + a | u t | p − 1 u t = b | u | q − 1 u in a bounded domain is studied, whereA = ( − Δ ) m, m ≥ 1 is a nature number, anda, b > 0 andp, q > 1 are real numbers. The existence of global solutions for this problem is proved by constructing the stable sets and shows the asymptotic stability of the global solutions as time goes to infinity by applying the multiplier method.