LONG TIME BEHAVIOR FOR SOLUTION OF INITIAL BOUNDARY VALUE PROBLEM OF ONE CLASS OF SYSTEMS WITH MULTIDIMENSIONAL INHOMOGENEOUS GBBM EQUATIONS

The following initial-boundary value problem for the systems with multidimensional inhomogeneous generalized Benjamin-Bona-Mahony ( GBBM ) equations is reviewed. The existence of global attractors of this problem was proved by means of a uniform priori estimate for time.     

GLOBAL ATTRACTOR FOR HASEGAWA-MIMA EQUATION

The long time behavior of solution of the Hasegawa-Mima equation with dissipation term was considered. The global attractor problem of the Hasegawa-Mima equation with initial periodic boundary condition was studied. Applying the uniform a priori estimates method, the existence of global attractor of this problem was proved, and also the dimensions of the global attractor was estimated.     

ON SOLUTIONS OF BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS WITH JUMPS, WITH UNBOUNDED STOPPING TIMES AS TERMINAL AND WITH NON-LIPSCHITZ COEFFICIENTS, AND PROBABILISTIC INTERPRETATION OF QUASI-LINEAR ELLIPTIC TYPE INTEGRO- DIFFERENTIAL

Ｉｔ’ｓｗｅｌｌ＿ｋｎｏｗｎｔｈａｔｔｈｅｓｏｌｕｔｉｏｎｓｏｆｂａｃｋｗａｒｄｓｔｏｃｈａｓｔｉｃｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓ(ＢＳＤＥｓ)ｐｌａｙａｎｉｍｐｏｒｔａｎｔｒｏｌｅｉｎｔｈｅｆｉｎａｎｃｉａｌｍａｒｋｅｔ(ＳｅｅＲｅｆ.[1]).ＷｉｔｈｕｎｂｏｕｎｄｅｄｓｔｏｐｐｉｎｇｔｉｍｅｓτａｓｔｅｒｍｉｎａｌｓｕｎｄｅｒｔｈｅＬｉｐｓｃｈｉｔｚｃｏｎｄｉｔｉｏｎｓａｎｄｃｏｎｄｉｔｉｏｎｔｈａｔｔｅｒｍｉｎａｌｓｓａｔｉｓｆｙＥ｜ξ｜2ｅＫ(τ∧Ｔ)≤ｃ0<∞,0≤Ｔ<∞ｏｒξ=0,Ｒｅｆｓ…     

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.     

Initial-boundary value problem of one class of nonlinear Schrödinger equations described in molecular crystals

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

Existence of the vortex solutions of some semilinear elliptic equations

The purpose is to extend the existence result of vortex solutions to semilinear elliptic equations for a large class of nonlinearities. M. I. Weinstein used variational techniques to show the existence of nodal solutions for the specific nonlinear term f(¦¦)=(1–¦¦²). An ordinary differential equation phase space setting is used to show the unique transverse intersection of unstable and stable manifolds which contain the solutions satisfying the necessary boundary conditions under certain assumptions on the nonlinearity.     

用边界元方法分析复合材料中的裂纹问题

利用层状材料的广义Klevin基本解,建立了计算三维层状材料中的裂纹边界元方法。采用边界元方法中的多区域方法和能反映均匀介质中裂纹尖端应力场和位移场特征的面力奇异单元。裂纹的应力强度因子由裂纹面上的位移经插值计算得到。算例分析表明,本文建议的方法可以获得较高的计算精度。     

Series solutions for steady unsaturated flow in irregular porous domains

For the most part, analytical solutions for steady unsaturated infiltration have been restricted to infinite and semi-infinite seepage geometries, using the quasi-linear approximation for the hydraulic conductivity. We provide analytical series methods to solve the steady quasi-linear flow equations, in finite irregular seepage geometries. Unlike the classical approach, the series method has been modified, to cater for arbitrary boundary geometry and surface recharge distributions. The matrix flux potential and the stream function both satisfy the same governing partial differential equation, and the stream function formulation is used to estimate the series coefficients. For a finite vadose zone, the stream function solution does not uniquely determine the matrix flux potential, when flux boundary conditions are used. Consequently, the stream function solution applies to a range of moisture distributions, for given infiltration and evapotranspiration rates through the surface.     

Regularity criteria for the 3D MHD equations in terms of the pressure

In this paper we consider the regularity criteria for weak solutions to the 3D MHD equations. It is proved that under the condition b being in the Serrin's regularity class, if the pressure p belongs to L^α,γ with or the gradient field of pressure p belongs to L^α,γ with on [0,T], then the solution remains smooth on [0,T].     

GENERALIZED MULTIVARIATE RIDGE REGRESSION ESTIMATE AND CRITERIA Q(e)FOR CHOOSING MATRIX K

When multicollinearity is present in a set of the regression variables,the leastsquare estimate of the regression coefficient tends to be unstable and it may lead toerroneous inference.In this paper,generalized ridge estimateβ(K)of the regression coefficientβ=vec(B)is considered in multivaiate linear regression model.The MSE of the aboveestimate is less than the MSE of the least square estimate by choosing the ridgeparameter matrix K.Moreover,it is pointed out that the Criterion MSE for choosingmatrix K of generalized ridge estimate has several weaknesses.In order to overcomethese weaknesses,a new family of criteria Q(c)is adpoted which includes the criterionMSE and criterion LS as its special case.The good properties of the criteria Q(c)areproved and discussed from theoretical point of view.The statistical meaning of thescale c is explained and the methods of determining c are also given.