EXPONENTIAL DECAY FOR A NONLINEAR VISCOELASTIC EQUATION WITH SINGULAR KERNELS

doi:10.1016/S0252-9602(12)60173-8

摘要/Abstract

摘要：

The nonlinear viscoelastic wave equation
|u_t|^ρ u_tt − Δu − Δu_tt +∫^t₀g(t − s)Δu(s)ds + |u|^p u = 0,
in a bounded domain with initial conditions and Dirichlet boundary conditions is consid-ered. 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.

关键词: viscoelastic wave equation, kernel, exponential decay, memory term, singu-lar kernel

Abstract:

Key words: viscoelastic wave equation, kernel, exponential decay, memory term, singu-lar kernel

中图分类号:

35B40

Shun-Tang Wu. EXPONENTIAL DECAY FOR A NONLINEAR VISCOELASTIC EQUATION WITH SINGULAR KERNELS[J]. 数学物理学报(英文版), 2012, 32(6): 2237-2246.

Shun-Tang Wu. EXPONENTIAL DECAY FOR A NONLINEAR VISCOELASTIC EQUATION WITH SINGULAR KERNELS[J]. Acta mathematica scientia,Series B, 2012, 32(6): 2237-2246.

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