On the Suitable Weak Solutions to the Boussinesq Equations in a Bounded Domain

ＯｎｔｈｅＳｕｉｔａｂｌｅＷｅａｋＳｏｌｕｔｉｏｎｓｔｏｔｈｅＢｏｕｓｓｉｎｅｓｑＥｑｕａｔｉｏｎｓｉｎａＢｏｕｎｄｅｄＤｏｍａｉｎＧｕｏＢｏｌｉｎｇ（郭柏灵）ＹｕａｎＧｕａｎｇｗｅｉ（袁光伟）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＰｈｙｓｉｃｓａｎ...     

The Initial-Boundary Value Problem for the Boussinesq Equations

ＴｈｅＩｎｉｔｉａｌ－ＢｏｕｎｄａｒｙＶａｌｕｅＰｒｏｂｌｅｍｆｏｒｔｈｅＢｏｕｓｓｉｎｅｓｑＥｑｕａｔｉｏｎｓｗｉｔｈＤａｔａｉｎＬ￣ＰＧｕｏＢｏｌｉｎｇ（郭柏灵），ＹｕａｎＧｕａｎｇｗｅｉ（袁光伟）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＰｈｙｓｉ...     

A Noteon Fuzzy Groups

ＡＮｏｔｅｏｎＦｕｚｚｙＧｒｏｕｐｓＡＮｏｔｅｏｎＦｕｚｚｙＧｒｏｕｐｓＭａｎｏｒａｊａｎ；ＫｕｍａｒＳｉｎｇｈ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＧｒａｍＢｈａｒｔｉｃｏｌｌｅｇｅ，Ｒａｍｇａｒｈ（Ｋａｉｍｕｒ），ＨＢＡＢＵＡ（Ｂｉｈ...     

Remarks on the Global Attractor of the Weakly Dissipative Benjamin－Ono Equation

ＲｅｍａｒｋｓｏｎｔｈｅＧｌｏｂａｌＡｔｔｒａｃｔｏｒｏｆｔｈｅＷｅａｋｌｙＤｉｓｓｉｐａｔｉｖｅＢｅｎｊａｍｉｎ－ＯｎｏＥｑｕａｔｉｏｎＧｕｏＢｏｌｉｎｇ（郭柏灵）ａｎｄＷｕＹｏｎｇｈｕｉ（吴永辉）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＰｈｙｓｉｃ...     

A singularly perturbed second order quasilinear BVP

ＡＳＩＮＧＵＬＡＲＬＹＰＥＲＴＵＲＢＥＤＳＥＣＯＮＤＯＲＤＥＲＱＵＡＳＩＬＩＮＥＡＲＢＶＰＬＩＮＷＵＺＨＯＮＧ（林武忠）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ,ＥａｓｔＣｈｉｎａＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ,Ｓｈａｎｇｈａｉ２０００６２...     

FREE BOUNDARY PROBLEM ARISING FROM EVAPORATION FROM POROUS MEDIUM

ＦＲＥＥＢＯＵＮＤＡＲＹＰＲＯＢＬＥＭＡＲＩＳＩＮＧＦＲＯＭＥＶＡＰＯＲＡＴＩＯＮＦＲＯＭＰＯＲＯＵＳＭＥＤＩＵＭＹＡＮＧＬＩＰＩＮＧ（杨力平）（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ＴｓｉｎｇｈｕａＵｎｉｖｅｒｓｉｔｙ，Ｂｅ...     

Theta Subgroups and the Solvability of FiniteGroups

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＤｅｆｉｎｉｔｉｏｎＡｌｌｇｒｏｕｐｓｔｒｅａｔｅｄａｒｅｆｉｎｉｔｅ．Ｉｎ［１］，Ｎ．Ｐ．ＭｕｋｈｅｒｊｅｅａｎｄＰ．Ｂｈａｔｔａｃｈａｒｙａｄｅｆｉｎｅｄｔｈｅｃｏｎｃｅｐｔｏｆθ－ｐａｉｒｓａｓｓｏｃｉａｔｅｄｔｏａｍａｘｉｍａｌｓｕｂｇｒｏｕｐＭｏｆａｇｒｏｕｐＧａｓｆｏｌｌｏｗｓ：ａθ－ｐａｉｒｆｏｒＭｉｓａｎｙｐａｉｒｏｆｓｕｂｇｒｏｕｐｓ（Ｃ，Ｄ）ｏｆＧｓｕｃｈｔｈａｔ（１）ＤＧ，Ｄ＜Ｃ，（２）〈Ｍ，Ｃ〉＝Ｇ，〈Ｍ，Ｄ〉＝Ｍａｎｄ（３）Ｃ／Ｄ…     

Bireflectionality of the Orthogonal Group over a Principal Ideal Domain

ＢｉｒｅｆｌｅｃｔｉｏｎａｌｉｔｙｏｆｔｈｅＯｒｔｈｏｇｏｎａｌＧｒｏｕｐｏｖｅｒａＰｒｉｎｃｉｐａｌＩｄｅａｌＤｏｍａｉｎＣｈｅｎＹｉｈｏｎｇ（陈一宏）（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ＢｅｉｊｉｎｇＩｎｓｔｉｔｕｔｅ...     

A CENTRAL LIMIT THEOREM FOR LATTICE GAUGE GIBBS RANDOM FIELDS

ＡＣＥＮＴＲＡＬＬＩＭＩＴＴＨＥＯＲＥＭＦＯＲＬＡＴＴＩＣＥＧＡＵＧＥＧＩＢＢＳＲＡＮＤＯＭＦＩＥＬＤＳＣＨＥＮＤＯＮＧＱＩＮＧ（陈冬青）（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ＴｓｉｎｇｈｕａＵｎｉｖｅｒｓｉｔｙ，Ｂｅｉｊｉ...     

Group Boolean algebras

ＧｒｏｕｐＢｏｏｌｅａｎＡｌｇｅｂｒａｓＷ．Ｂ．ＶａｅａｎｔｈａＫａｎｄａｓａｍｇ（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＩｎｄｉａｎＩｎｓｔｉｔｕｔｅｏｆＴｅｃｈｎｏｌｏｇｙ，Ｉｎｄｉａ）ＧｒｏｕｐＢｏｏｌｅａｎＡｌｇｅｂｒａｓ／Ｗ．Ｂ．ＶａｅａｎｔｈａＫａｎ...     

The Global Attractors for Damped Generalized Coupled Nonlinear Wave Equations

The existence of global attractors for the periodic initial value problem of damped generalized coupled nonlinear wave equations is proved. We also get the estimates of the upper bounds of Hausdorff and fractal dimensions for the global attractors by means of a uniformly priori estimates for time.     

Dimension estimate of the global attractor for a semi-discretized chemotaxis-growth system by conservative upwind finite-element scheme

In this paper we continue systematic study of the dimension estimate of the global attractors for the chemotaxis-growth system and its finite-element approximations. Utilizing a conservative upwind finite-element scheme we managed significantly to improve dimension estimates with respect to the chemotactic parameter.     

The Global Attractors for the Periodic Initial Value Problem of Generalized Kuramoto-Sivashinsky Type Equations in Multi-dimensions

The existence of global attractors for the periodic initial value problem of generalized Kuramoto-Sivashinsky type equations in multi-dimensions is proved. We also get the estimates of the upper bounds of Hausdorff and fractal dimensions for the global attractors by means of a uniform priori estimates for time.     

The Global Attractors for the Periodic Initial Value Problem For a Coupled Non-linear Wave Equation

The existence of global attractors of the periodic initial value problem for a coupled non-linear wave equation is proved. We also get the estimates of the upper bounds of Hausdorff and fractal dimensions for the global attractors by means of uniform a priori estimates for time.     

Long time behavior for damped generalized coupled nonlinear wave equations.Ⅰ.Bounded domain

Introduction In [1], the authors established the unique ekistence of the smooth solution for the couplednonlinear equations. These were proposed to describe the iateraction process of internal longwaves. In [2], Ito proposed a recursion operator by which he inferred that the equations possess infinitely many symmetries and constants of motion. In [3], He established the ealstenceo f a smooth solution to the system of coupled nonlinear KdV equationl41. We remark thatSchonbekls] dealt' with a…     

耗散的广义对称正则长波方程周期初值问题的整体吸引子

该文考虑了带有耗散项的广义对称正则长波方程解的长时间性态.证明了周期初值问题整体吸引子的存在性,用关于时间的一致先验估计获得整体吸引子的Hausdorff和分形维数的上界估计.     

Plate models with state-dependent damping coefficient and their quasi-static limits

We study long-time dynamics of a class of plate models with a state-dependent damping coefficient and their quasi-static limits. We first present the problem in abstract form and then prove the existence of finite-dimensional global attractors and their upper semicontinuity in the quasi-static limit, i.e., in the case when the mass density of plate tends to zero. Our proofs involve a recently developed method based on “compensated” compactness and quasi-stability estimates. As an application we consider the nonlinear Kirchhoff, von Karman and Berger plate models with different types of boundary conditions and damping coefficients. Our results can be also applied to the nonlinear wave equations in an arbitrary dimension.     

The Global Attractors for the Dissipative Generalized Hasegawa-Mima Equation

The long time behavior of solutions of the generalized Hasegawa-Mima equation with dissipation term is considered. The existence of global attractors of the periodic initial value problem is proved, and the estimate of the upper bound of the Hausdorff and fractal dimensions for the global attractors is obtained by means of uniform a priori estimates method.     

Global attractors for the initial value problems of Cohn-Hilliard equations on compact manifolds

In this paper we establish some theorems which are concerned with the equivalent norms of Sobolev spaces on a Riemannian manifold. Using the theorems we prove the existence of global attractors for the initial value problem of Cahn-Hilliard equations. The estimates of the upper bounds of Hausdorff and fractal dimensions for the global attractors are also obtained.     

Bounds for attractors and the existence of homoclinic orbits in the lorenz system

Frequency estimates are derived for the Lyapunov dimension of attractors of non-linear dynamical systems. A theorem on the localization of global attractors is proved for the Lorenz system. This theorem is applied to obtain upper bounds for the Lyapunov dimension of attractors and to prove the existence of homoclinic orbits in the Lorenz system.