Decay rate for a class of viscoelasticity equation with nonlinear damping on the boundary

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:340

Article

Han, Xianjun^1,2  Xue, Hongxia³ 

[1] Zhengzhou Univ, Dept Math, Zhengzhou 450052, Peoples R China

[2] Zhengzhou Inst Light Ind, Dept Informat & Comp Sci, Zhengzhou 450002, Peoples R China

[3] Zhengzhou Inst Aeronaut Ind, Dept Math & Phys, Zhengzhou 450015, Peoples R China

关键词: viscoelasticity equation;    nonlinear damping;    decay rate;   

DOI  :  10.1016/j.jmaa.2007.08.015

来源: Elsevier

【 摘 要 】

In this paper we study the equation of viscoelasticity u(tt) - u(xxt) - F(u(x))(x)=f(x, t) with the nonlinear damping term on the boundary. Making use of the so-called energy perturbation method and a comparison inequality we prove the relationship between decay rate of solutions and f(x, t), that is, they have the same exponential decay or algebraic decay for the case F(s)=s+vertical bar s vertical bar(alpha) (-) (2) (alpha >= 2), and for the case F(s)=vertical bar s vertical bar(alpha - 2) (alpha > 2), they have the same algebraic decay. (c) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

Free