含线性阻尼的2D非自治g-Navier-Stokes方程的拉回吸引子

讨论了无界区域上含线性阻尼的2D非自治g-Navier-Stokes方程的拉回吸引子,通过验证共圈的拉回公.吸收集的存在性和拉回公一渐近紧性,证明了含线性阻尼的2D非自治g-Navier-Stokes方程的拉回吸引子的存在性,并给出了拉回吸引子的Fractal维数估计.     

强阻尼波方程解的整体存在性和一致衰减性

这篇文章研究一类带非线性源项和非线性边界阻尼项的强阻尼波 方程强解和弱解的整体存在性和唯一性,进而也讨论解的一致衰减.     

带有时滞项的超三次弱阻尼波方程一致吸引子的存在性

该文考虑带有时滞项的弱阻尼波方程一致吸引子的存在性,其中非线性项的增长次数大于3而小于5.通过构造能量泛函并结合收缩函数方法得到过程Ug(t,7τ),g∈H-(g0)在CH10(Ω)×CL2(Ω)中一致吸引子的存在性.     

有界区域上2D非自治g-Navier-Stokes方程的拉回吸引子

通过研究拉回渐近紧性来讨论有界区域上2D非自治g-Navier-Stokes方程的拉回吸引子的存在性,给出了一种验证拉回吸引子存在性的新方法.     

完全非线性抛物型方程解的正则性

本文证明了:若完全非线性一致抛物型方程ut-F(D2u)=0有Liouville性质,则它的任何C1 1,1 1/2(Q1)粘性解u-定属于C2 α,1 α/2(Q1/2)且ut一定属于     

非自治的Schrdinger方程的吸引子

研究2维的非自治非线性Schrdinger方程长时间的动力学行为,证明了一致吸引子的存在性,并给出了该一致吸引子Hausdorff维数的上界,     

非自治的Schrdinger方程的吸引子

研究 2维的非自治非线性Schr dinger方程长时间的动力学行为·　证明了一致吸引子的存在性 ,并给出了该一致吸引子Hausdorff维数的上界·     

带非线性阻尼的粘弹方程解的整体存在性和一致衰减性

研究带有非线性阻尼的粘弹方程,得到了弱解整体存在性和一致指数衰减性.     

非自治的Schroedinger方程的吸引子

研究2维的非自治非线性Schroedinger方程长时间的动力学行为。证明了一致吸引子的存在性,并给出了该一致吸引子Hausdorff维数的上界。     

带线性记忆和结构阻尼的非自治Kirchhoff型板方程的一致吸引子

本文试图研究带线性记忆和结构阻尼的非自治Kirchhoff型板方程的一致吸引子的存在性.为此,引入一个新的变量η,将先验估计与收缩函数的方法相结合,证明一致有界吸收集和一致渐近紧性,最终得到一致吸引子的存在性.     

二维自治g-Navier-Stokes系统的全局渐近行为研究

研究了有界区域上二维自治g-Navier-Stokes系统的双全局吸引子,利用非紧性测度方法,给出了一种验证其存在性的新方法.得出二维自治g-Navier-Stokes方程在有界区域上有一个非空、紧可逆H_g一V_g全局吸引子这一结论.     

General decay of energy for a viscoelastic equation with nonlinear damping

In this paper we are concerned with a nonlinear viscoelastic equation with nonlinear damping. The general uniform decay of the energy is obtained. Copyright © 2008 John Wiley & Sons, Ltd.     

Global solvability and uniform decays of solutions to quaslinear equation with nonlinear boundary dissipation

A n-dimensional quasiliner wave equation with nonlinear boundary dissipation is considered. Global existence, uniqueness and uniform decay rates are established for the model, under the assumption that the H¹(Ω)xL₂(Ω') norms of the initial data are sufficiently small. The result presented in this paper extends/generalizes those obtained those obtained recently in (13), where, by contrast, interior nonlinear damping was considered; and those obtained in (31), where the one-dimensional wave equation with linear boundary damping was treated.     

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

A viscoelastic equation with Balakrishnan-Taylor damping and nonlinear boundary/interior sources is considered in a bounded domain. Under appropriate assumptions imposed 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.     

Remark on the regularity of the global attractor for the wave equation with nonlinear damping

In this paper, we study the 3D wave equation with nonlinear interior damping. We prove that the global attractor of the semigroup generated by this equation has optimal regularity.     

Global existence and uniform decay for a nonlinear viscoelastic equation with damping

In this paper we investigate a nonlinear viscoelastic equation with linear damping. Global existence of weak solutions and the uniform decay estimates for the energy have been established.     

强耗散可拉伸梁方程解的一致衰减性（英文）

This paper investigates the existence and uniform decay of global solutions to the initial and boundary value problem with clamped boundary conditions for a nonlinear beam equation with a strong damping.     

Uniform boundary stabilization of a wave equation with nonlinear acoustic boundary conditions and nonlinear boundary damping

We consider a wave equation with nonlinear acoustic boundary conditions. This is a nonlinearly coupled system of hyperbolic equations modeling an acoustic/structure interaction, with an additional boundary damping term to induce both existence of solutions as well as stability. Using the methods of Lasiecka and Tataru for a wave equation with nonlinear boundary damping, we demonstrate well-posedness and uniform decay rates for solutions in the finite energy space, with the results depending on the relationship between (i) the mass of the structure, (ii) the nonlinear coupling term, and (iii) the size of the nonlinear damping. We also show that solutions (in the linear case) depend continuously on the mass of the structure as it tends to zero, which provides rigorous justification for studying the case where the mass is equal to zero.     

Decay Rates of Interactive Hyperbolic-Parabolic PDE Models with Thermal Effects on the Interface

We consider coupled PDE systems comprising of a hyperbolic and a parabolic-like equation with an interface on a portion of the boundary. These models are motivated by structural acoustic problems. A specific prototype consists of a wave equation defined on a three-dimensional bounded domain Ω coupled with a thermoelastic plate equation defined on Γ ₀—a flat surface of the boundary \partial Ω . Thus, the coupling between the wave and the plate takes place on the interface Γ ₀. The main issue studied here is that of uniform stability of the overall interactive model. Since the original (uncontrolled) model is only strongly stable, but not uniformly stable, the question becomes: what is the ``minimal amount' of dissipation necessary to obtain uniform decay rates for the energy of the overall system? Our main result states that boundary nonlinear dissipation placed only on a suitable portion of the part of the boundary which is complementary to Γ <sub>0</sub>, suffices for the stabilization of the entire structure. This result is new with respect to the literature on several accounts: (i) thermoelasticity is accounted for in the plate model; (ii) the plate model does not account for any type of mechanical damping, including the structural damping most often considered in the literature; (iii) there is no mechanical damping placed on the interface Γ <sub>0</sub>; (iv) the boundary damping is nonlinear without a prescribed growth rate at the origin; (v) the undamped portions of the boundary \partial Ω are subject to Neumann (rather than Dirichlet) boundary conditions, which is a recognized difficulty in the context of stabilization of wave equations, due to the fact that the strong Lopatinski condition does not hold. The main mathematical challenge is to show how the thermal energy is propagated onto the hyperbolic component of the structure. This is achieved by using a recently developed sharp theory of boundary traces corresponding to wave and plate equations, along with the analytic estimates recently established for the co-continuous semigroup associated with thermal plates subject to free boundary conditions. These trace inequalities along with the analyticity of the thermoelastic plate component allow one to establish appropriate inverse/ recovery type estimates which are critical for uniform stabilization. Our main result provides ``optimal' uniform decay rates for the energy function corresponding to the full structure. These rates are described by a suitable nonlinear ordinary differential equation, whose coefficients depend on the growth of the nonlinear dissipation at the origin. \par Accepted 12 May 2000. Online publication 6 October 2000.