Long Time Behavior of Nonlinear Strain Waves in Elastic Waveguides

The initial-boundary value problem of the propagation of nonlinear longitudinal elastic waves in an initially strained rod is considered. The rod is assumed to interact with the surrouding elastic and viscous external medium. The long time behavior of solutions is derived ancl global attractors in E_1 space is obtained.     

NONLINEAR STABILITY OF RAREFACTION WAVES FOR A RATE-TYPE VISCOELASTIC SYSTEM

51.IntroductionInthispaper,westudythefollowingrate-typeviscoelasticsystem,i.e.,wherevand(--p)denotestrainandstress,uisrelatedtotheparticlevelocity,EisapositiveconstantcalledthedynamicYOung'smodulus,T>0isarelaxationtime.Thissystemwasproposedinfi6]tointroducearelaxationapproximationtothefollowingsystemSincethesystem(1.2)canbeobtainedfrom(1.1)byanexpansionprocedureasthefirstorder,itisnaturaltoexpectthatthesolutionof(1.1)convergestothatof(1.2)asT-0.However,thezerolimitconvergencehasnotbeenestabl…     

非线性应变波耦合组的指数吸引子

本文研究了一在应变波耦合组所生成的半群性质,通过算子解和构造进紧不变集,得到了该耦合组的紧的指数吸引子。     

非线性特征值问题正解的全局分歧

讨论非线笥特征值问题正解的全局分歧,即关于方程ｕ＝Ｆ（λ,ｕ）的分歧,其中ｕ限制在锥上,Ｆ（λ,．）按由锥诱导的序为正;给出了分歧存在的必要和充分条件及分歧枝的全局结构,并将所得到的结论应用到一个半线性椭圆型方程组中去。     

无界区域R3上的非线性应变波方程与薛定谔方程藕合方程组的指数吸引子

本文研究了无界区域R~3上的非线性应变波方程与薛定谔方程藕合方程组.运用带权空间构造一类紧算子和算子分解的方法,得到了该方程在无界区域R3上的H~2×H~2×H~1(R~3)中拥有一个指数吸引子.     

A SYSTEM OF BOUNDARY INTEGRO-DIFFERENTIAL EQUATIONS FOR HARMONIC ELASTIC WAVES IN R3

Here we derive a new representation of the derivative of the double-layer potential for harmonic elastic waves in R3.Based on this new representation,the Neumann internal problem and the Neumann external problem of harmonic elastic waves are reduced to a system of boundary integro-differential equations,which is convenient for numerical approximation.     

A LOCAL ATTRACTOR FOR A NONLINEAR WAVE EQUATION ARISING IN ELASTIC WAVEGUIDE MODEL

This paper studies the asymptotic behavior of solutions to the initial boundary value problem for a nonlinear wave equation arising in an elastic waveguide model. It proves that under rather mild conditions on g the related solution semigroup possesses a local attractor.     

EXISTENCE AND NONEXISTENCE OF GLOBAL SOLUTION OF NONLINEAR PARABOLIC EQUATION WITH NONLINEAR BOUNDARY CONDITION

ＥＸＩＳＴＥＮＣＥＡＮＤＮＯＮＥＸＩＳＴＥＮＣＥＯＦＧＬＯＢＡＬＳＯＬＵＴＩＯＮＯＦＮＯＮＬＩＮＥＡＲＰＡＲＡＢＯＬＩＣＥＱＵＡＴＩＯＮＷＩＴＨＮＯＮＬＩＮＥＡＲＢＯＵＮＤＡＲＹＣＯＮＤＩＴＩＯＮ￥ＷＵＹＯＮＧＨＵＩ；ＷＡＮＧＭＩＮＧＸＩＮＡｂｓｔｒ...     

一类三阶非线性系统的全局稳定性

本文运用“类比法”，构造了一类三阶非线性系统的李雅普诺夫函数，从而推出了该系统的零解全局渐近稳定的条件。     

一类非线性差分方程的持久性与全局吸引性

本文研究了差分方程ｘ（ｎ＋１）＝ｘｐｎｆ（ｘｎ，ｘ（ｎ－ｋ１），…，ｘ（ｎ－ｋｒ））的持久性与全局吸引性，解决了文［３］提出的两个研究课题，所得结果包含了文［３］的相应结果．     

一类非线性差分人口模型解的全局渐近稳定性

考虑非线性差分方程其中a＞0，b≤0，c＞0．方程（1）是时滞人口模型的离散模拟．J．W．Rodrigus[7]研究了方程（1）当k＝0时正平衡解的振动性和全局渐过稳定性．本文我们获得了方程（1）当k＞0时正平衡解全局渐近稳定的充分条件，从而补充了文[7]中结论．     

一维非线性泛函微分方程的全局吸引性

本文获得了如下非线性泛函微分方程ｘ＇（ｔ）＝ｘ（ｔ）ｆ（ｘｔ），ｔ≥０的所有正解以其正平衡状态为全局吸引子的一族充分条件，推广了Ｌａｄａｓ等人的方法。将结果应用于几类时滞Ｌｏｇｉｓｔｉｃ方程，改进了文献［１，２，５］的相应结果。     

ON THE EXISTENCE OF GLOBAL ATTRACTOR FOR A CLASS OF INFINITE DIMENSIONAL DISSIPATIVE NONLINEAR DYNAMICAL SYSTEMS

By means of a nonstandard estimation about the energy functional, the authors prove the existence of a global attractor for an abstract nonlinear evolution equation. As an application, the existence of a global attractor for some nonlinear reaction-diffusion equations with some distribution derivatives in inhomogeneous terms is obtained.     

非线性波动与神经传播混合型方程的整体紧吸引子

本文研究非线性波动与神经传播混合型方程u_tt＝u_xxt＋σ（u_x）_x－h（u）u_t-f（u）＋g（x）初边值问题的整体吸引子.在σ∈C~2,σ＇（s）＞σo＞0及h（s）∈C~1,－Co＜）且∫~u_oh（s）sds＞0）条件下我们得到了与该方程相应的动力系统整体紧吸引子的存在性，并证明了它具有有限的Hausdorff维数和fractal维数．