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1.
We study in this paper the global existence and exponential decay of solutions of the non‐linear unidimensional wave equation with a viscoelastic boundary condition. We prove that the dissipation induced by the memory effect is strong enough to secure global estimates, which allow us to show existence of global smooth solution for small initial data. We also prove that the solution decays exponentially provided the resolvent kernel of the relaxation function, k decays exponentially. When k decays polynomially, the solution decays polynomially and with the same rate. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
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In this paper we prove the existence of global decaying H2 solutions to the Cauchy problem for a wave equation with a nonlinear dissipative term by constructing a stable set in H1(?n ). (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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This paper is concerned with the decay rate of solutions for a quasilinear wave equation with viscosity. We use a so-called energy perturbation method to establish decay rate of solutions in terms of energy norm for a class of nonlinear functions. With the help of a comparison lemma of differential inequalities, we establish a relationship between decay rate of solutions and f . 相似文献
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ABSTRACTThis paper is concerned with the decay property of a nonlinear viscoelastic wave equation with linear damping, nonlinear damping and source term. Under weaker assumption on the relaxation function, we establish a general decay result, which extends the result obtained in Messaoudi [Exponential decay of solutions of a nonlinearly damped wave equation. Nodea-Nonlinear Differ Equat Appl. 2005;12:391–399]. 相似文献
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In this article, we investigate a nonlinear viscoelastic equation with nonlinear localized damping and velocity-dependent material density. We prove the global existence of weak solutions and general decay of the energy by using the Faedo–Galerkin method [Z.Y. Zhang and X.J. Miao, Global existence and uniform decay for wave equation with dissipative term and boundary damping, Comput. Math. Appl. 59 (2010), pp. 1003–1018; J.Y. Park and J.R. Kang, Global existence and uniform decay for a nonlinear viscoelastic equation with damping, Acta Appl. Math. 110 (2010), pp. 1393–1406] and the perturbed energy method [Zhang and Miao (2010); X.S. Han, and M.X. Wang, Global existence and uniform decay for a nonlinear viscoelastic equation with damping, Nonlinear Anal. TMA. 70 (2009), pp. 3090–3098], respectively. Furthermore, for certain initial data and suitable conditions on the relaxation function, we show that the energy decays exponentially or polynomially depending the rate of the decay of the relaxation function. This result is an improvement over the earlier ones in the literature. 相似文献
6.
Tran-Vu Ngo;Bao-Dung Dao;Mirelson M. Freitas; 《Mathematische Nachrichten》2024,297(1):378-413
In this paper, we consider the initial boundary value problem of the generalized pseudo-parabolic equation containing viscoelastic terms and associated with Robin conditions. We establish first the local existence of solutions by the standard Galerkin method. Then, we prove blow-up results for solutions when the initial energy is negative or nonnegative but small enough or positive arbitrary high initial energy, respectively. We also establish the lifespan and the blow-up rate for the weak solution by finding the upper bound and the lower bound for the blow-up times and the upper bound and the lower bound for the blow-up rate. For negative energy, we introduce a new method to prove blow-up results with a sharper estimate for the upper bound for the blow-up times. Finally, we prove both the global existence of the solution and the general decay of the energy functions under some restrictions on the initial data. 相似文献
7.
研究带有阻尼项的非线性波动方程(1.1),得出在初值满足一定条件时,方程的整体解存在,且解的能量是指数衰减的. 相似文献
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The initial boundary value problem for a system of viscoelastic wave equations of Kirchhoff type with strong damping is considered. We prove that, under suitable assumptions on relaxation functions and certain initial data, the decay rate of the solutions energy is exponential. 相似文献
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ThisresearchissupportedbytheNationalNaturalScienceFoundationofChina.1.IntroductionInthispaper,weconsiderthefollowinginitial--boundaryvalueproblemwhereQ~fix(o,co),aQ=aflx(o,co),fiisaboundeddomaininEuclideanspaceR"(n22)withsmoothboundaryonandac=(u.,,'Iu..)denotesthegradientoffunctionu(x).Weassumethefunctionsal(x,t,u,p)(i=1,2,',n)anda(x,t,u,p)arelocallyH5ldercontinuousonfix(0,co)suchthatwherealtuandparepositiveconstants,m,aZIa3.hi,b2,alIadZ20,or321areconstants,m*E[0,m 2),hi16z/0,afl m*/… 相似文献
10.
We study the initial boundary value problem for the nonlinear viscoelastic wave equation with strong damping term and dispersive term. By introducing a family of potential wells we not only obtain the invariant sets, but also prove the existence and nonexistence of global weak solution under some conditions with low initial energy. Furthermore, we establish a blow-up result for certain solutions with arbitrary positive initial energy (high energy case) 相似文献
11.
In this paper, a problem which arises in a class of viscoelasticity is considered. We obtain the decay rate of the energy, for certain class of relaxation functions not necessarily exponentially or polynomially decaying to zero. 相似文献
12.
The purpose of this article is to prove the energy decay of the mixed problem for a nonlinear viscoelastic rod equation with dynamic boundary conditions. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
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Jum‐Ran Kang 《Mathematical Methods in the Applied Sciences》2016,39(11):2953-2964
In this paper, we study a viscoelastic wave equations of Kirchhoff type with acoustic boundary conditions. For a viscoelastic wave equations of Kirchhoff type without strong damping, we prove an explicit and general decay rate result, using some properties of the convex functions. 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. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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In this paper, we investigate the exponential time decay rate of solutions toward traveling waves for the Cauchy problem of generalized Benjamin-Bona-Mahony-Burgers equations
(E) 相似文献
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A. V. Gasnikov 《Computational Mathematics and Mathematical Physics》2006,46(12):2136-2153
The time asymptotic behavior of the solution to the Cauchy problem for a quasilinear parabolic equation is analyzed. Such problems are encountered, for example, in gas dynamics and transport flow simulation. A.M. Il’in and O.A. Oleinik’s well-known results are extended to a wider class of equations in which the time derivative of the unknown function is multiplied by a fixed-sign function of the former. The results have found applications in mathematical economics. 相似文献
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Salah Boulaaras Alaeddin Draifia Khaled Zennir 《Mathematical Methods in the Applied Sciences》2019,42(14):4795-4814
This work deals with the study of a new class of nonlinear viscoelastic Kirchhoff equation with Balakrishnan‐Taylor damping and logarithmic nonlinearity. A decay result of the energy of solutions for the problem without imposing the usual relation between a certain relaxation function and its derivative is established. This result generalizes earlier ones to an arbitrary rate of decay, which is not necessarily of exponential or polynomial decay. 相似文献
19.
非线性Kirchhoff型波动方程描述了竖直方向上的波动.利用近似FaedoGalerkin的方法通过先验估计和一种新的验证紧性的方法(条件C)讨论了这类波动方程强解的全局吸引子. 相似文献