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Acta Mathematica Scientia 2017年第5期37卷 1453-1471页

作者： Vamna BOUKHATEM Benyattou BENABDERRAHMANE Laboratory of Pure and Applied Mathematics University of LaghouatP.O.Box 37GLaghouat 03000Algeria Laboratory of Pure and Applied Mathematics Mohamed Boudiaf UniversityM'sila 28000Algeria

A variable coefficient viscoelastic equation with a time-varying delay in the boundary feedback and acoustic boundary conditions and nonlinear source term is *** suitable assumptions, general decay results of the energy are established via suitable Lyapunov functionals and some properties of the convex functions. Our result is obtained without imposing any restrictive growth assumption on the damping term and the elements of the matrix A and the kernel function g.

关键词： acoustic boundary conditions general decay time-varying delay variable coefficients viscoelastic equation

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GENERAL DECAY OF SOLUTIONS FOR A viscoelastic equation WITH BALAKRISHNAN-TAYLOR DAMPING AND NONLINEAR BOUNDARY DAMPING-SOURCE INTERACTIONS

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Acta Mathematica Scientia 2015年第5期35卷 981-994页

作者：吴舜堂 General Education Center National Taipei University of Technology

A viscoelastic equation with Balakrishnan-Taylor damping and nonlinear boundary/interior sources is considered in a bounded domain. Under appropriate assumptions ira- posed on the source and the damping, we establish uniform decay rate of the solution energy in terms of the behavior of the nonlinear feedback and the relaxation function, without setting any restrictive growth assumptions on the damping at the origin and weakening the usual assumptions on the relaxation function.

关键词： Balakrishnan-Taylor damping global existence general decay relaxation function viscoelastic equation

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General Decay of Solutions in a viscoelastic equation with Nonlinear Localized Damping

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Journal of Mathematical Research with Applications 2012年第1期32卷 53-62页

作者： Xiao Jun SONG 1,Rong ZENG 2,,Chun Lai MU 2 1.College of Mathematics and Information,China West Normal University,Sichuan 637002,P.R.China 2.College of Mathematics and Statistics,Chongqing University,Chongqing 401331,P.R.China College of Mathematics and Information China West Normal University Sichuan 637002 College of Mathematics and Statistics Chongqing University Chongqing 401331

In this paper,we consider the following viscoelastic equation u tt- △u +∫t 0 g(t-s)△u(s)ds + a(x)u t + u |u|r = 0 with initial condition and Dirichlet boundary *** decay property of the energy function closely depends on the properties of the relaxation function g(t) at *** the previous works of [3,7,11],it was required that the relaxation function g(t) decay exponentially or polynomially as t → +∞.In the recent work of Messaoudi [12,13],it was shown that the energy decays at a similar rate of decay of the relaxation function,which is not necessarily dacaying in a polynomial or exponential *** by [12,13],under some assumptions on g(x),a(x) and r,and by introducing a new perturbed energy,we also prove the similar results for the above equation.

关键词： general decay viscoelastic equation relaxation function.

On the General Stability of a viscoelastic Wave equation with an Integral Condition

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Acta Mathematicae Applicatae Sinica 2020年第4期36卷 857-869页

作者： FARIDA BELHANNACHE SALIM A.MESSAOUDI Department of Mathematics and LMPA Laboratory University Mohamed Seddik Ben Yahia-JijelJijel 18000Algeria Department of Mathematics University of SharjahSharjah 27272UAE

We consider a nonlocal boundary value problem for a viscoelastic equation with a Bessel operator and a weighted integral condition and we prove a general decay *** also give an example to show that our general result gives the optimal decay rate for ceratin polynomially decaying relaxation *** result improves some other results in the literature.

关键词： integral condition viscoelastic equation general decay Bessel operator

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Global Existence and Blow Up of Solutions in a Cauchy viscoelastic Problem

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Journal of Partial Differential equations 2018年第3期31卷 224-236页

作者： LIU Gongwei TIAN Shuying College of Science Henan University of Technology Zhengzhou 450001 China. School of Science Wuhan University of Technology Wuhan 430070 China.

The Cauchy problem for a viscoelastic equation with nonlinear damping and source terms is considered. We establish the nonexistence result of global solutions with initial energy controlled above by a critical value by modifying the method introduced in a work by Autuori et al. in 2010. Then we establish global existence for arbitrary initial data or the energy in potential well. These improve earlier results in the literatures.

关键词： Cauchy problem viscoelastic equation global existence blow up