The periodic unfolding method for the heat equation in perforated domains

We study the heat equation with non-periodic coefficients in periodically perforated domains with a homogeneous Neumann condition on the holes. Using the time-dependent unfolding method, we obtain some homogenization and corrector results which generalize those by Donato and Nabil(2001).     

带不完美界面的双曲问题均匀化的一个注记

本文研究了一类二分区域上的具有非周期系数的双曲问题.利用周期Unfolding方法,得到了均匀化及其矫正结果,推广了Donato,Faella和Monsurrò的工作.     

超双曲型方程特征问题的一个注记

<正> 超双曲型方程定解问题的提法,长期为人们所关注.1948年,讨论了四变元齐次超双曲型方程的特征问题.1961年,推广到2n 个变元.前者得到 Fourier 展开形式解,后者利用积分几何的结果得到积分表达式解.     

非自治退化抛物-双曲方程的柯西问题

非自治退化抛物-双曲型方程可以描述许多自然现象.主要研究这类方程的柯西问题,建立了动力学公式,在对流函数、扩散函数适当光滑性的基础上,证明了该问题动力学解的存在唯一性.     

带不完美界面的双曲问题均匀化的一个注记（英文）

本文研究了一类二分区域上的具有非周期系数的双曲问题.利用周期Unfolding方法,得到了均匀化及其矫正结果,推广了Donato,Faella和Monsurrò的工作.     

关于非自治Benjiamin-Bona-Mohony方程拉回吸引子的一个注记(英文）

In this paper,we show the existence of pullback attractors for the nonautonomous Benjamin-Bona-Mahony equations by establishing the pullback uniform asymptotically compactness.     

退化抛物-双曲方程动力学解的唯一性

主要研究系数显含有时间和空间变量的退化抛物-双曲型方程柯西问题动力学解的唯一性.首先推广了这种类型方程的动力学公式,在给定系数适当的光滑性条件下,得到了动力学解的唯一性.     

半线性双曲波动方程的H~1-Galerkin扩展混合元方法(英文)

An H1-Galerkin expanded mixed finite element method is discussed for a class of second order semi-linear hyperbolic wave equations. By using the mixed formulation, we can get the optimal approximation for three variables: the scalar unknown, its gradient and its flux(coefficient times the gradient), simultaneously. We also prove the existence and uniqueness of semi-discrete solution. Finally, we obtain some numerical results to illustrate the efficiency of the method.     

一般无界区域中带有阻尼的三维可压缩欧拉方程

考虑在一般的三维无界区域中的具有滑移边界条件的带有阻尼的可压缩欧拉方程.当初始值接近平衡态时,获得了全局存在性和唯一性.同时,研究了在半空间情形下系统的衰减率.证明了经典解的L~2范数以(1+t)~(-3/4)衰减到常值背景解.     

一个耦合双曲-抛物系统的全局光滑解

考虑一个源自生物学的耦合双曲-抛物模型的初边值问题.当动能函数为非线性函数以及初始值具有小的L~2能量但其H~2能量可能任意大时,得到了初边值问题光滑解的全局存在性和指数稳定性.而且,如果假定非线性动能函数满足一定的条件,在对初值没任何小条件假定下得到光滑解的全局存在性.通过构造一个新的非负凸熵和做精细的能量估计得到了结果的证明.     

Homogenization of Stationary Navier-Stokes Equations in Domains with 3 Kinds of Typical Holes

The aim of this paper is to investigate homogenization of stationary NavierStokes equations with a Dirichlet boundary condition in domains with 3 kinds of typical holes. For space dimension $N$ =2 and 3, we utilize a unified approach for 3 kinds of tiny holes to accomplish the homogenization of stationary Navier-Stokes equations. The unified approach due to Lu [1] is mainly based on the uniform estimates with respect to ε for the generalized cell problem inspired by Tartar.     

Homogenization in perforated domains with mixed conditions

In this paper we study the asymptotic behaviour of the Laplace equation in a periodically perforated domain of R ⁿ , where we assume that the period is ε and the size of the holes is of the same order of greatness. An homogeneous Dirichlet condition is given on the whole exterior boundary of the domain and on a flat portion of diameter if (, if n=2) of the boundary of every hole, while we take an homogeneous Neumann condition elsewhere.     

Uniqueness of Solutions on the Whole Time Axis to the Navier-Stokes Equations in Unbounded Domains

We consider the uniqueness of bounded continuous L^{3, ∞}-solutions on the whole time axis to the Navier-Stokes equations in 3-dimensional unbounded domains. Here, L^{p, q} denotes the scale of Lorentz spaces. Thus far, uniqueness of such solutions to the Navier-Stokes equations in unbounded domain, roughly speaking, is known only for a small solution in BC(?; L^{3, ∞}) within the class of solutions which have sufficiently small L^∞(L^{3, ∞})-norm. In this paper, we discuss another type of uniqueness theorem for solutions in BC(?; L^{3, ∞}) using a smallness condition for one solution and a precompact range condition for the other one. The proof is based on the method of dual equations.     

三维薄区域上MHD方程的渐进分析

在强解全局存在的基础上, 得到了三维薄区域上MHD方程的解(u,h)对任意时间t≥ 0的渐进分析. 当区域厚度ε小时, MHD方程的强解(u,h)可形式展开为u=ū(t)+up+U, h=h(t)+hp+H, t ≥0或u=ū(t)+us+U＊,h=h(t)+hs+H＊,t ≥0,其中(u,h) 是2D-3C MHD 方程的解, (u_p,h_p) 是P-S MHD 方程的解, u,h 分别是两个Stokes方程的解, (U,H),(U＊,H＊)是仅依赖于初始数据的两个函数对. (U,H)和(U＊,H＊)关于区域厚度\varepsilon是小的, (u_p,h_p)和u,h更小;证明了上述形式展开的收敛性.     

Homogenization for Degenerate Quasilinear Parabolic Equations of Second Order

In this paper we study the homogenization of degenerate quasilinear parabolic equations: where a(t, y, a, λ) is periodic in (t, y).     

A Note on the Maximum Principle for Second-Order Elliptic Equations in General Domains

We make a further advance concerning the maximum principle for second-order elliptic operators. We investigate in particular a geometric condition, first considered by Berestycki Nirenberg Varadhan, that seems to be natural in view of the application of the boundary weak Harnack inequality, on which our argument is based. Setting it free from some technical assumptions, apparently needed in earlier papers, we significantly enlarge the class of unbounded domains where the maximum principle holds, compatibly with the first-order term.     

Semilinear Elliptic Equations on Thin Network-Shaped Domains with Variable Thickness

We study semilinear elliptic equations in a thin domain which is shaped like a network and degenerate into a geometric graph when a certain parameter tends to zero. It is shown by using a comparison technique that a solution of the equation in the network-shaped domain approaches a solution of an associated limit equation on the graph. Conversely, when the limit equation on the graph has a solution, we prove the existence of a solution of the PDE in the network-shaped domain which converges to the solution of the limit equation.     

一类抛物型方程边界条件的均匀化模型及证明

设伪抛物问题边界 Ω =Γ可表为Γ =Γ0 ∪Γ1,对任意ε>0 ,将Γ1分为Γε1和Γε1,并在其上给出不同的边界条件 ;讨论了几种当Γε1的每一连通分支的直径或沿某方向的直径随ε趋于零而趋于零时的相应解的极限性态 .     

Homogenization of the Maxwell Equations: Case I. Linear Theory

The Maxwell equations in a heterogeneous medium are studied. Nguetseng's method of two-scale convergence is applied to homogenize and prove corrector results for the Maxwell equations with inhomogeneous initial conditions. Compactness results, of two-scale type, needed for the homogenization of the Maxwell equations are proved.