On two-dimensional large-scale primitive equations in oceanic dynamics （Ⅱ）

The initial boundary value problem for the two-dimensional primitive equations of largescale oceanic motion in geophysics is considered sequetially. Here the depth of the ocean is positive but not always a constant. By Faedo-Galerkin method and anisotropic inequalities, the existence and uniqueness of the global weakly strong solution and global strong solution for the problem are obtained. Moreover, by studying the asymptotic behavior of solutions for the above problem, the energy is exponential decay with time is proved.     

Homoclinic orbits for some （2＋1）-dimensional nonlinear Schrodinger-like equations

Chaos is closely associated with homoclinic orbits in deterministic nonlinear dynamics. In this paper, analytic expressions of homoclinic orbits for some （2＋1）- dimensional nonlinear Schrodinger-like equations are constructed based on Hirota＇s bilinear method, including long wave-short wave resonance interaction equation, generalization of the Zakharov equation, Mel＇nikov equation, and g-Schrodinger equation are constructed based on Hirota＇s bilinear method.     

On two-dimensional large-scale primitive equations in oceanic dynamics(Ⅰ)

The initial boundary value problem for the two-dimensional primitive equations of large scale oceanic motion in geophysics is considered.It is assumed that the depth of the ocean is a positive constant.Firstly,if the initial data are square integrable,then by Fadeo-Galerkin method,the existence of the global weak solutions for the problem is obtained.Secondly, if the initial data and their vertical derivatives axe all square integrable,then by Faedo-Galerkin method and anisotropic inequalities,the existerce and uniqueness of the giobal weakly strong solution for the above initial boundary problem axe obtained.     

On two-dimensional large-scale primitive equations in oceanic dynamics(Ⅱ)

The initial boundary value problem for the two-dimensional primitive equations of largescale oceanic motion in geophysics is considered sequetially.Here the depth of the ocean is positive but not always a constant.By Faedo-Galerkin method and anisotropic inequalities,the existence and uniqueness of the global weakly strong solution and global strong solution for the problem are obtained.Moreover,by studying the asymptotic behavior of solutions for the above problem,the energy is exponential decay with time is proved.     

Existence and uniqueness of solutions to the dynamic equations for koiter shells

１ＴｈｅＰｒｏｐｏｓａｌｏｆＰｒｏｂｌｅｍＷｅｃｏｎｓｉｄｅｒａｆａｍｉｌｙｏｆｌｉｎｅａｒｅｌａｓｔｉｃｓｈｅｌｓｏｆｔｈｉｃｋｎｅｓ２ε,ａｌｈａｖｉｎｇｔｈｅｓａｍｅｍｉｄｄｌｅｓｕｒｆａｃｅＳ＝φ（ω）Ｒ３,ｗｈｅｒｅωＲ２ｉｓａｂｏｕｎ...     

Homogenized equations for steady heat conduction in composite materials with dilutely-distributed impurities

In this paper.by using the two-space method,homogenizedequations for steady heat conduction in the composite ma-terial cylinders with dilutely-distributed elliptic cylin-ders of impurities are derived.and the ezplicit ezpres-sions for the corresponding effective heat conductivity ofthose which are concerned are obtained.It is also shownthat the macroscopic heat conduction is anisotropic whenthe cross-sections of the impurity cylinders are unidirec-tionally oriented and isotropic when the angular distribu-tion of the cross-sections is uniform.     

On a class of quasilinear Schrodinger equations

A type of quasilinear Schrodinger equations in two space dimensions which describe attractive Bose-Einstein condensates in physics is discussed. By establishing the property of the equation and applying the energy method, the blowup of solutions to the equation are proved under certain conditions. At the same time, by the variational method, a sutficient condition of global existence which is related to the ground state of a classical elliptic equation is obtained.     

New models of Cahn-Hilliard-Gurtin equations

In this article, we further generalize the models of Cahn-Hilliard equations proposed by Gurtin and based on a balance law for microforces. We then study the existence and uniqueness of solutions and the boundedness of the order parameter.Received: 26 May 2003, Accepted: 29 August 2003, Published online: 3 February 2004PACS: 02.30.Jr, 64.75. + g Correspondence to: M. Efendiev     

Level set methods based on distance function

Some basic problems on the level set methods were discussed, such as the method used to preserve the distance junction , the existence and uniqueness of solution for the level set equations. The main contribution is to prove that in a neighborhood of the initial zero level set, the level set equations with the restriction of the distance function have a unique solution, which must be the signed distance function with respect to the evolving surface. Some skillful approaches were used: Noticing that any solution for the original equation was a distance function, the original level set equations were transformed into a simpler alternative form. Moreover, since the new system was not a classical one, the system was transformed into an ordinary one, for which the implicit function method was adopted.     

Initial-boundary value problem of one class of nonlinear Schr(o)dinger equations described in molecular crystals

In this paper,we study the initial-boundary value problem of one class of nonlinear Schr(o)dinger equations described in molecular crystals.Furthermore,the existence of the global solution is obtained by means of interpolation inequality and a priori estimation.     

Stability of Schr(o)dinger-Poisson type equations

Variational methods are used to study the nonlinear Schr(o)dinger-Poisson type equations which model the electromagnetic wave propagating in the plasma in physics. By analyzing the Halniltonian property to construct a constrained variational problem, the existence of the ground state of the system is obtained. Furthermore, it is shown that the ground state is orbitally stable.