Asymptotic Behavior of Stochastic Strongly Damped Wave Equation with Multiplicative Noise

In this paper we study the asymptotic dynamics of the stochastic strongly damped wave equation with multiplicative noise under homogeneous Dirichlet boundary condition. We investigate the existence of a compact random attractor for the random dynamical system associated with the equation.

Uniform Exponential Attractors for Non-Autonomous Strongly Damped Wave Equations

In this paper, we study the existence of exponential attractors for strongly damped wave equations with a time-dependent driving force. To this end, the uniform H?lder continuity is established to the variation of the process in the phase apace. In a certain parameter region, the exponential attractor is a uniformly exponentially attracting time-dependent set in the phase apace, and is finite-dimensional no matter how complex the dependence of the external forces on time is. On this basis, we also obtain the existence of the infinite-dimensional uniform exponential attractor for the system.

Existence of Multiple Equilibrium Points in Global Attractor for the Strongly Damped Wave Equations

The aim of this paper is to study the long-term behavior of strongly damped wave equations with a Lyapunov function. Using the theory established by estimating the Z2 index of some sets and the idea of invariant sets of semi-flow,the properties of the global attractor for strongly damped wave equation are discussed. The existence of multiple equilibrium points in global attractor for strongly damped wave equations with critical growth of nonlinearity is obtained. And under some additional condition, the infinite dimension of the attractor is proven.

On the Strongly Damped Wave Equations with Critical Nonlinearities

We study the strongly damped wave equations with critical nonlinearities. By choosing suitable state spaces, we prove sectorial property of the operator matrix together with its adjoint operator, investigate the associated interpolation and extrapolation spaces, analysis the criticality of the nonlinearity with critical growth, and study the higher spatial regularity of the Y-regular solution by bootstrapping.

Asymptotic Behavior of Stochastic Strongly Wave Equation on Unbounded Domains

We study the asymptotic behavior of solutions to the stochastic strongly damped wave equation with additive noise defined on unbounded domains. We first prove the uniform estimates of solutions, and then establish the existence of a random attractor.

Mixed Spectral and Pseudospectral Methods for a Nonlinear Strongly Damped Wave Equation in an Exterior Domain

The aim of this paper is to develop the mixed spectral and pseudospectral methods for nonlinear problems outside a disc,using Fourier and generalized Laguerre functions.As an example,we consider a nonlinear strongly damped wave equation.The mixed spectral and pseudospectral schemes are proposed.The convergence is proved.Numerical results demonstrate the efficiency of this approach.

非自治记忆型强阻尼波方程的拉回指数吸引子

研究了非自治记忆型强阻尼波方程的拉回指数吸引子存在问题。利用耗散过程的一致挤压性质,对拉回吸引子的每个集合延伸扩展,使得它的一致有界吸收集有有限分形维数,进而利用分解方法验证过程的ω-渐近紧性,并且拉回指数吸引子以指数速率拉回吸引相空间中的每个子集,最后证明了拉回指数吸引子的存在性。

带有非局部强阻尼的Kirchhoff型波方程的时间依赖全局吸引子

对于带有非局部强阻尼和非线性扰动的Kirchhoff型波方程,研究了其在时间依赖空间中解的长时间行为.运用收缩函数的方法验证了过程的渐近紧性,得到了时间依赖全局吸引子的存在性.

四阶具强阻尼非线性波动方程解的整体存在性与不存在性

研究四阶具强阻尼非线性波动方程utt-△u＋△^2u-α△ut=f（u）的初边值问题.利用位势井方法,得到了问题整体解存在性与不存在性的最佳条件（门槛结果）.

具有强阻尼项和非线性阻尼项的波动方程解的整体存在性和有限时间爆破(英文)

本文考虑了一类具有强阻尼和非线性阻尼项的波动方程:utt-Δu-ωΔut+μ|ut|m-2ut=|u|p-2u,其中p>2,m>2,ω=μ=1.利用变分法和紧性引理,本文证明了基态驻波解的存在性.并且得到了解的整体存在和爆破条件.

一类强阻尼非线性波动方程的初边值问题

研究一类强阻尼非线性波动方程的初边值问题,模型方程为utt-α△ut-△u=f(u),u(x,0)=u0(x),ut(x,0)=u1(x) x∈Ω,u｜ Ω=0,t>0,其中f(u)的符号与位移的符号相反,应用能量估计的方法,该问题得到了很好的解决.当源项与位移的符号相同时,即f(u)=｜u｜p-1u,仅用能量估计的方法无法得到解的先验估计.本文应用位势井的方法,对这种类型的问题作进一步的探讨,得到了问题整体弱解的存在性.推广了已有的结果.

关于方程u_(tt)-Δu_t-Δu_(tt)=f(u)的某些注记

研究方程utt-Δu-Δut-Δutt=f(u)的初边值问题，指出在文献[1]中，为证明此问题整体强解的存在性与唯一性所加的增长条件|f'(s)|≤A|s|^x+B,0<α≤2/n-2可以改进为0<α≤4/n-2，并将这一改进的结果推广到所有n>3．

关于方程u_(tt)-△u-△u_t-△u_(tt)=f(u)的一个注记

研究方程utt-△u-△ut-△utt=f(u)的初边值问题,纠正了文[1]中关于解的渐近性质结果中的一个错误.

强阻尼波动方程的非协调元超收敛分析

利用导数转移方法和构造插值算子技巧,讨论了强阻尼波动方程在各向异性条件下的1个非协调元逼近,给出了强阻尼波动方程在半离散格式下精确解与近似解之间的误差估计和超逼近特性.最后,利用插值后处理方法得到了方程的整体超收敛结果.

非线性黏性波动方程强解的存在性

文章我们着重讨论以下具有边界阻尼的非线性黏性波动方程强解的存在性.设Ω是Rn的具有光滑边界Γ=Γ0∪Γ1的星形有界区域,这里Γ0与Γ1是不相交闭集,ν为外向单位法向量.在Ω上研究了具有边界阻尼项的非线性黏性波动方程ytt-Δy+∫0th(t-τ)Δy(τ)dτ+F(x,t,y,Δy)=0,(x,t)∈Ω×(0,∞);y=0,(x,t)∈Γ1×(0,∞);y /ν-∫0th(t-τ)y/ν(τ)dτ+byt=0,(x,t)∈Γ0×(0,∞);y(x,0)=y0(x),yt(x,0)=y1(x),x∈Ω.这里b>0.我们利用Faedo-Galerkin方法证明上述问题强解的存在性.

一类四阶非线性波动方程解的爆破与衰减

本文研究了非线性阻尼项与源项的竞争对具有强阻尼项的四阶波动方程解的影响.利用不动点原理和势井方法给出了方程局部弱解存在唯一性满足的条件,证明了当m<p且初始能量E(0)<0时,解将在有限时间内爆破.同时对m,p的大小关系不加任何限制但存在t_0使0<E(t_0)<d的情况下,利用稳定集,研究了整体解的存在性,并得到了解的能量衰减估计.最后借助修正的能量泛函,指出当m≥p时弱解也是整体存在的,推广并改进了文献[1-6]中的结果.

四阶强阻尼非线性波动方程的整体W^(k,p)解

证明四阶强阻尼非线性波动方程的初边值问题utt-Δu -αΔut-εΔutt+ f ( u) =0 (α≥ 0 ,ε>0 ) ,u( x,0 ) =u0 ( x) , ut( x,0 ) =u1( x) ,u| Ω =0的整体广义解的存在惟一性 .利用“逐次磨光法”证明其整体 W2 ,p与 Wk,p的存在性 ,并讨论其整体古典解的存在性 .

一类四阶非线性波动方程柯西问题解的爆破

研究非线性阻尼项与源项的竞争对具有强阻尼项的四阶波动方程解的影响.得到源项强于阻尼项时(即当m<p),初始能量为正,且初始数据满足一定条件时,解将在有限时间内爆破,并得到解生命跨度的上界估计.

Kirchhoff型波方程的时间依赖全局吸引子

对于带有强阻尼和非线性扰动的Kirchhoff波方程,研究它在时间依赖空间中解的长时间行为.运用收缩函数的方法验证过程的渐近紧性,得到时间依赖全局吸引子的存在性.

具有阻尼和非线性对数源项的波方程能量衰减

研究具有线性强阻尼、非线性弱阻尼和非线性对数源项波方程解的存在性和能量衰减。在合适的假设条件下,通过势阱方法和Lyapunov泛函方法分别证明了在初始能量小于阱深、等于阱深两种情形下系统能量的指数衰减。