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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

general decay OF SOLUTIONS FOR A VISCOELASTIC EQUATION WITH NONLINEAR DAMPING AND SOURCE TERMS

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Acta Mathematica Scientia 2011年第4期31卷 1436-1448页

作者： Wu Shuntang general Education Center National Taipei University of Technology Taipei 106 China

The initial boundary value problem for a viscoelastic equation ｜ u t ｜ ρ u tt △u-△u tt ＋ t 0 g（ts）△u（s）ds ＋｜ u t ｜ m u t = ｜ u ｜ p u in a bounded domain is considered, where ρ, m, p 〉 0 and g is a n... 详细信息

The initial boundary value problem for a viscoelastic equation ｜ u t ｜ ρ u tt △u-△u tt ＋ t 0 g（ts）△u（s）ds ＋｜ u t ｜ m u t = ｜ u ｜ p u in a bounded domain is considered, where ρ, m, p 〉 0 and g is a nonnegative and decaying function. The general uniform decay of solution energy is discussed under some conditions on the relaxation function g and the initial data by adopting the method of [14, 15, 19]. This work generalizes and improves earlier results in the literature.

关键词： global existence asymptotic behavior general decay

general decay FOR A QUASILINEAR SYSTEM OF VISCOELASTIC EQUATIONS WITH NONLINEAR DAMPING

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Acta Mathematica Scientia 2012年第4期32卷 1321-1332页

作者： Jong Yeoul Park Sun Hye Park Department of Mathematics Pusan National UniversityBusan 609-735 South Korea

In this paper, we consider a system of coupled quasilinear viscoelastic equa- tions with nonlinear damping. We use the perturbed energy method to show the general decay rate estimates of energy of solutions, which extends some existing results concerning a general decay for a single equation to the case of system, and a nonlinear system of viscoelastic wave equations to a quasilinear system.

关键词： general decay coupled quasilinear equations viscoelastic equations perturbed energy method

general decay FOR A DIFFERENTIAL INCLUSION OF KIRCHHOFF TYPE WITH A MEMORY CONDITION AT THE BOUNDARY

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Acta Mathematica Scientia 2014年第3期34卷 729-738页

作者： Jum-Ran KANG Department of Mathematics Dong-A UniversityBusan 604-714Korea

In this article, we consider a differential inclusion of Kirchhoff type with a memory condition at the boundary. We prove the asymptotic behavior of the corresponding solutions. For a wider class of relaxation functions, we establish a more general decay result, from which the usual exponential and polynomial decay rates are only special cases.

关键词： general decay differential inclusion boundary value problem memory term relaxation function

general decay FOR A POROUS-THERMOELASTIC SYSTEM WITH MEMORY: THE CASE OF NONEQUAL SPEEDS

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Acta Mathematica Scientia 2013年第1期33卷 23-40页

作者： Salim A.MESSAOUDI Abdelfeteh FAREH Departement of Mathematics and Statistics King Fahd University of Petroleum and MineralsDhahran 31261Saudi Arabia Departement of Mathematics Faculty of Science and TechnologyUniversity of El-OuedBP78939000El OuedAlgeria

The aim of this paper is to establish a general decay result for a one-dimensional porous elastic system with different speeds of wave propagation in the presence of macrotem- perature effect and visco-porous dissipat... 详细信息

关键词： general decay visco-porous dissipation non equal speeds

general decay OF A TRANSMISSION PROBLEM FOR KIRCHHOFF TYPE WAVE EQUATIONS WITH BOUNDARY MEMORY CONDITION

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Acta Mathematica Scientia 2014年第5期34卷 1395-1403页

作者： Sun Hye PARK Center for Education Accreditation Pusan National University

In this paper, we investigate the influence of boundary dissipation on the de-cay property of solutions for a transmission problem of Kirchhoff type wave equation with boundary memory condition. By introducing suitable energy and Lyapunov functionals, we establish a general decay estimate for the energy, which depends on the behavior of relaxation function.

关键词： transmission problem Kirchhoff type general decay memory term relaxationfunction

general decay for a Thermoelastic Problem of a Microbeam with Gurtin-Pipkin Thermal Law

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Acta Mathematicae Applicatae Sinica 2022年第2期38卷 426-440页

作者： Dong-qin CHEN Wen-jun LIU Zhi-jing CHEN School of Mathematics and Statistics Nanjing University of Information Science and TechnologyNanjing 210044China

In this paper,we study the well-posedness and the asymptotic stability of a one-dimensional thermoelastic microbeam system,where the heat conduction is given by Gurtin-Pipkin thermal *** first establish the well-posedness of the system by using the semigroup arguments and Lumer-Phillips *** then obtain an explicit and general formula for the energy decay rates through perturbed energy method and some properties of the convex functions.

关键词： microbeam system Gurtin-Pipkin thermal law well-posedness general decay

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

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.

general Energy decay of Solutions for a Weakly Dissipative Kirchhoff Equation with Nonlinear Boundary Damping

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Acta Mathematicae Applicatae Sinica 2017年第2期33卷 401-408页

作者： Amir Peyravi Department of Mathematics College of Sciences Shiraz University Shiraz 71467-13565 Iran

In this article, we study the weak dissipative Kirchhoff equation under nonlinear damping on the boundary We prove a general energy decay property for solutions in terms of coefficient of the frictional boundary damping. Our result extends and improves some results in the literature such as the work by Zhang and Miao （2010） in which only exponential energy decay is considered and the work by Zhang and Huang （2014） where the energy decay has been not considered.

关键词： Kirchhoff equation general decay boundary damping