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

作者：Han Xianjun^*; Xue Hongxia

来源：Journal of Mathematical Analysis and Applications, 2008, 340(1): 322-333.

DOI：10.1016/j.jmaa.2007.08.015

• viscoelasticity equation
• nonlinear damping
• decay rate

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.

• 出版日期2008-4-1
• 单位郑州大学