Random region function and its applications

This paper establishes some basic concepts of the random region, and random region function. From these concepts, and the existence of a random stable point of a random region function of the random region the necessary and suficient conditions for the existence of a random stable centre of any random region are defined.     

非线性奇性椭圆边值问题解的存在性

设X=(x_1,x_2,…,X_n)∈R~n,E_0是半空间x_n≥0.Ω(?)E_o是有界的光滑区域,(?)Ω=S_1US_2,此处S_1在超平面X_n=0上,而S_2整个地位于X_n>0上.讨论非线性奇性椭圆边值问题     

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 two‐dimensional unsteady incompressible fluid flow in an infinite strip

In this paper, we study two‐dimensional incompressible fluid flow in an infinite strip. The stream function form of Navier–Stokes equation is considered, which keeps the physical boundary condition and avoids some difficulties in numerical simulations. The existence and uniqueness of global solution are proved. Some results on the regularity of solution are obtained. Copyright © 2000 John Wiley & Sons, Ltd.     

浅谈二元函数的带Peano型余项的Taylor公式

本文讨论了二元函数带Peano型余项的泰勒公式及唯一性,例说其应用.     

Singular properties of solutions for a parabolic equation with variable exponents and logarithmic source

This paper deals with a parabolic $p\left(x\right)$-Laplace equation with logarithmic source $u^{q\left(x\right)}logu$. The singular properties of solutions are determined completely by classifying the initial energy. Moreover, we obtain a new extinction rate of solutions, where the order of the extinction rate is greater than the maximum of variable exponent $q\left(x\right)$. This kind of extinction rate could reflect the influence of logarithmic functions on the extinction of solutions more reasonably.     

On solutions of anisotropic elliptic equations with variable exponent and measure data

ABSTRACT

The Dirichlet problem in arbitrary domains for a wide class of anisotropic elliptic equations of the second order with variable exponent nonlinearities and the right-hand side as a measure is considered. The existence of an entropy solution in anisotropic Sobolev spaces with variable exponents is established. It is proved that the obtained entropy solution is a renormalized solution of the considered problem.