Random Attractor for Non-autonomous Stochastic Strongly Damped Wave Equation on Unbounded Domains

In this paper we study the asymptotic dynamics for the nonautonomous stochastic strongly damped wave equation driven by additive noise defined on unbounded domains. First we introduce a continuous cocycle for the equation and then investigate the existence and uniqueness of tempered random attractors which pullback attract all tempered random sets.     

Finite-Element Methods for a Strongly Damped Wave Equation

Error estimates of optimal order are proved for semidiscreteand completely discrete finite-element methods for a linearwave equation with strong damping, arising in viscoelastic theory.It is demonstrated that the exact solution may be interpretedin terms of an analytic semigroup, and as a result that, althoughthe solution has essentially the spatial regularity of its initialdata, it is infinitely differentiable in time for t>0. Theestimates for the spatially discrete method are derived by energyarguments. Rational approximation of analytic semigroups isdiscussed in a general setting, by means of spectral representation,and the results are used to analyse the completely discreteschemes. Both smooth (and compatible) and less smooth data areconsidered.     

强阻尼波动方程吸引子的正则性及其逼近

该文研究强阻尼波动方程的初边值问题．利用线性主算子在相空间中生成的解析半群的性质,证明了解的光滑效应,这个现象与弱阻尼波动方程的情形大不相同．由此作者得到了吸引子的正则性,并象自伴情形那样构造了近似惯性流形．     

Neumann边界条件下强阻尼波动方程的一维全局吸引子

本文主要考虑齐次Neumann边界条件下强阻尼波动方程的全局吸引子的存在性．利用渐近时间周期微分方程的极限集的性质,证明了在一定的参数范围内,齐次Neumann边界条件下强阻尼波动方程存在一维全局吸引子,是一条水平曲线．     

Neumann边界条件下强阻尼波动方程的一维全局吸引子

本文主要考虑齐次Neumann边界条件下强阻尼波动方程的全局吸引子的存在性．利用渐近时间周期微分方程的极限集的性质，证明了在一定的参数范围内，齐次Neumann边界条件下强阻尼波动方程存在一维全局吸引子，是一条水平曲线．     

Error Estimates for Mixed Finite Element Methods for Sobolev Equation

1 IntroductionLet fl be a bounded domain in R2 with Lipschitz continuous boundaxy 0fl. For thed0 < T < co, we consider the fo1lowing initial-boun'lar}-ralue problem for thc Sobolevequation:where ut denotes the time derivative of the function (1. Vu denotes the gradient of thefunction u, and divv denotes the divergence of the vect{Jr tulued function v, a1 b1, f, anduo are known functions.The standard finite element method for (1.1) (1.3) llas received considerable attentionand is well studied…     

强阻尼半线性波动方程的全局吸引子

本文讨论一类带强阻尼项的半线性波动方程的全局吸引子的存在性．首先给出了方程解的存在唯一性定理，建立了解的C°-半群；然后运用Hale提出的a-收缩理论，证明了该类方程存在全局吸引子．     

On a Strongly Damped Wave Equation for the Flame Front

In two-dimensional free-interface problems, the front dynamics can be modeled by single parabolic equations such as the Kuramoto-Sivashinsky equation （K-S）. However, away from the stability threshold, the structure of the front equation may be more involved. In this paper, a generalized K-S equation, a nonlinear wave equation with a strong damping operator, is considered. As a consequence, the associated semigroup turns out to be analytic. Asymptotic convergence to K-S is shown, while numerical results illustrate the dynamics.     

粘弹性波动方程的H~1-Galerkin混合有限元方法误差估计(英文)

H1-Galerkin mixed methods are proposed for viscoelasticity wave equation.Depending on the physical quantities of interest,two methods are discussed.The optimal error estimates and the proof of the existence and uniqueness of semidiscrete solutions are derived for problems in one space dimension.And the methods don＇t require the LBB condition.     

具有阻尼的半线性波动方程解的衰减估计

研究具有阻尼的半线性波动方程的初边值问题u_(tt)-△u+βu_t=|u|~(p-1)u,x∈Ω,t>0u(x,0)=u_0(x),u_t(x,0)=u_1(x),x∈Ωu|_((?)Ω)=0,t≥0其中γ为正常数,Ω■R~n为有界域,当n≥3时,1相似文献   

Regularization of a two-dimensional strongly damped wave equation with statistical discrete data

In this paper, we consider an inverse problem for a strongly damped wave equation in two dimensional with statistical discrete data. Firstly, we give a representation for the solution and then present a discretization form of the Fourier coefficients. Secondly, we show that the solution does not depend continuously on the data by stating a concrete example, which makes the solution be not stable and thus the present problem is ill-posed in the sense of Hadamard. Next, we use the trigonometric least squares method associated with the Fourier truncation method to regularize the instable solution of the problem. Finally, the convergence rate of the error between the regularized solution and the sought solution is estimated and also investigated numerically.     

On the Properties of the Solution of a Strongly Degenerate Parabolic Equation

ＯｎｔｈｅＰｒｏｐｅｒｔｉｅｓｏｆｔｈｅＳｏｌｕｔｉｏｎｏｆａＳｔｒｏｎｇｌｙＤｅｇｅｎｅｒａｔｅＰａｒａｂｏｌｉｃＥｑｕａｔｉｏｎＣｈｅｎｇＦｕｘｉａ（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ＴｓｉｎｇｈｕａＵｎｉｖｅｒｓｉｔ...     

具有非线性记忆项的耗散波动方程的整体吸引子

LetΩRn be a bounded domain with a smooth boundary.We consider the longtime dynamics of a class of damped wave equations with a nonlinear memory term utt+αut-△u-∫0t 0μ(t-s)|u(s)| βu(s)ds + g(u)=f.Based on a time-uniform priori estimate method,the existence of the compact global attractor is proved for this model in the phase space H10(Ω)×L2(Ω).     

任意维数的强阻尼非线性波动方程（Ⅰ）—初边值问题

本文研究任意维数的强阻非线性波动方程ｕｔｔ－ａΔｕｔ－Δｕ＝ｆ（ｕ）具第一类齐边界条件的初值问题，设ｆ∈Ｃ＾１，ｆ＾１（ｕ）上方有界，且当ｎ≥４时存在常数Ａ，Ｂ和ｐ，使｜ｆ＾１（ｕ）｜≤Ａ｜ｕ｜＾ｐ＋Ｂ，其中０＜ｐ≤４／（ｎ－４）（ｎ＞４）：０＜ｐ＜∞（ｎ＝４），得到唯一整体强解，从而改进和推广了已知结果。     

Exponential Decay of Energy for a Logarithmic Wave Equation

In this paper we consider the initial boundary value problem for a class of logarithmic wave equation. By constructing an appropriate Lyapunov function, we obtain the decay estimates of energy for the logarithmic wave equation with linear damping and some suitable initial data. The results extend the early results.     

一类具记忆项的非线性强阻尼双曲方程解的爆破性

利用一个特殊不等式得到一类具记忆项的非线性阻尼双曲方程解的爆破条件.方程描述了具记忆时滞的粘弹性梁问题.     

非线性波动方程的各向异性有限元方法

研究了非线性波动方程的各向异性有限元方法,得到了半离散格式下的最优误差估计.