BLOW－UP AND DIE－OUT OF SOLUTIONS OF NONLINEAR PSEUDO-HYPERBOLIC EQUATIONS OF GENERALIZED NERVE CONDUCTION TYPE

This paper considers the initial boundary value problems with three types of the boundary conditions for nonlinear pseudo-hyperbolic equations of generalized nerve conduction type, using foe eigenfunction method, the conditions for which the solutions blow-up and die-out in the finile time are got.

Nonconforming <i>H</i>¹-Galerkin Mixed Finite Element Method for Pseudo-Hyperbolic Equations

Based on H1-Galerkin mixed finite element method with nonconforming quasi-Wilson element, a numerical approximate scheme is established for pseudo-hyperbolic equations under arbitrary quadrilateral meshes. The corresponding optimal order error estimate is derived by the interpolation technique instead of the generalized elliptic projection which is necessary for classical error estimates of finite element analysis.

Superconvergence Analysis of Splitting Positive Definite Nonconforming Mixed Finite Element Method for Pseudo-hyperbolic Equations

In this paper, a new splitting positive definite nonconforming mixed finite element method is proposed for pseudo-hyperbolic equations, in which a quasi-Wilson quadrilateral element is used for the flux p, and the bilinear element is used for u. Superconvergence results in ｜｜·｜｜div,h norm for p and optimal error estimates in L2 norm for u are derived for both semi-discrete and fully discrete schemes under almost uniform meshes.

单位圆盘上Bergman圆的性质

运用单位圆盘上Pseudo-hyperbolic度量的性质,得到Bergman圆的欧式结构,欧式圆盘与Bergman圆的关系以及Bergman圆上全纯映射的性质。这些性质表明了全纯映射、对合自同构以及Bergman圆之间的密切联系,其在多复变函数理论和函数空间的研究中有理论意义。

AD GALERKIN ANALYSIS FOR NONLINEAR PSEUDO-HYPERBOLIC EQUATIONS

AD (Alternating direction) Galerkin schemes for d-dimensional nonlinear pseudo-hyperbolic equations are studied. By using patch approximation technique, AD procedure is realized, and calculation work is simplified. By using Galerkin approach, highly computational accuracy is kept. By using various priori estimate techniques for differential equations, difficulty coming from non-linearity is treated, and optimal H1 and L2 convergence properties are demonstrated. Moreover, although all the existed AD Galerkin schemes using patch approximation are limited to have only one order accuracy in time increment, yet the schemes formulated in this paper have second order accuracy in it. This implies an essential advancement in AD Galerkin analysis.

A Sufficient Condition for Interolation by Functions in A^P(φ) (1

Let φ be a normal function on [0,1) and A'(φ)(1<P<∞) Bergman space on the unit disk, weighted with φ~P(|·|)/(1-|·|~2).A sufficient condition for interpolation by functions in A^P(φ) is obtained by controlling norms of linear operators.

INITIAL VALUE PROBLEM FOR A CLASS OF NONLINEAR PSEUDO-HYPERBOLIC EQUATIONS

The existence of global weak solutions to the periodic boundary problem or the initial value problem for the nonlinear Pseudo-hyperbolic equation u_(tt)-[a_1+a_2(u_x)^(2m)]u_(xx)-a_3u_(xxt)=f(x,t,u,u_x) is proved by the method of the vanishing of the additional diffusion terms, Leray-Schauder's fixedpoint argument and Sobolev's estimates,where m≥1 is a natural number and a_i>0(i=1,2,3)are constants.

BMOA(Dλ)函数的几个问题

本文用伪双曲度量刻划了单位圆盘上双曲BMOA函数的几个特征。

Smoothness of invariant manifolds and foliations for in nite dimensional random dynamical systems--Dedicated to Professor Shantao Liao

In this paper,we investigate the smoothness of invariant manifolds and foliations for random dynamical systems with nonuniform pseudo-hyperbolicity in Hilbert spaces.We discuss on the effect of temperedness and the spectral gaps in the nonuniform pseudo-hyperbolicity so as to prove the existence of invariant manifolds and invariant foliations,which preserve the CN,τ;(ω)Holder smoothness of the random system in the space variable and the measurability of the random system in the sample point.Moreover,we also prove that the stable foliation is CN-1;(ω)in the base point.