EXPONENTIAL DECAY FOR A NONLINEAR VISCOELASTIC EQUATION WITH SINGULAR KERNELS

被引：2
|
作者：
Wu, Shun-Tang [1 ]
机构：
[1] Natl Taipei Univ Technol, Gen Educ Ctr, Taipei 106, Taiwan
来源：
ACTA MATHEMATICA SCIENTIA | 2012年 / 32卷 / 06期
关键词：
viscoelastic wave equation; kernel; exponential decay; memory term; singular kernel; WAVE-EQUATION; EXISTENCE; STABILITY;
D O I：
10.1016/S0252-9602(12)60173-8
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The nonlinear viscoelastic wave equation vertical bar u(t)vertical bar (rho) u(tt) - Delta u - Delta u(tt) + integral(t)(0) g(t - s)Delta u(s)ds + vertical bar u vertical bar(p) u = 0, in a bounded domain with initial conditions and Dirichlet boundary conditions is considered. We prove that, for a class of kernels g which is singular at zero, the exponential decay rate of the solution energy. The result is obtained by introducing an appropriate Lyapounov functional and using energy method similar to the work of Tatar in 2009. This work improves earlier results.
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页码：2237 / 2246
页数：10
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