THE SINGULAR LIMIT OF SECOND-GRADE FLUID EQUATIONS IN A 2D EXTERIOR DOMAIN

In this paper, we consider the second-grade fluid equations in a 2D exterior domain satisfying the non-slip boundary conditions. The second-grade fluid model is a wellknown non-Newtonian fluid model, with two parameters: α, which represents the length-scale,while ν > 0 corresponds to the viscosity. We prove that, as ν, α tend to zero, the solution of the second-grade fluid equations with suitable initial data converges to the one of Euler equations, provided that ν = o(α^(4/3)). Moreover, the convergent rate is obtained.

EXISTENCE AND NONEXISTENCE OF GLOBAL POSITIVE SOLUTIONS FOR DEGENERATE PARABOLIC EQUATIONS IN EXTERIOR DOMAINS

This article deals with the degenerate parabolic equations in exterior domains and with inhomogeneous Dirichlet boundary conditions. We obtain that pc = （σ ＋ m ）n / （ n-σ- 2 ） is its critical exponent provided max{-1, [ （1- m ）n- 2] / （ n ＋ l ） } 〈 σ 〈 n- 2. This critical exponent is not the same as that for the corresponding equations with the boundary value 0, but is more closely tied to the critical exponent of the elliptic type degenerate equations. Futhermore, we demonstrate that if max（1, σ ＋ m） 〈 p 〈 pc, then every positive solution of the equations blows up in finite time; whereas for p 〉 pc, the equations admit global positive solutions for some boundary values and initial data. Meantime, we also demonstrate that its positive solutions blow up in finite time provided n〈σ＋2.

LOW MACH NUMBER LIMIT ON EXTERIOR DOMAINS

This paper is concerned with the low Mach number limit for the compressible Navier-Stokes equations in an exterior domain. We present here an approach based on Strichartz estimate defined on a non trapping exterior domain and we will be able to show the compactness and strong convergence of the velocity vector field.

GLOBAL EXISTENCE FOR THE NONHOMOGENEOUS QUASILINEAR WAVE EQUATION WITH A LOCALIZED WEAKLY NONLINEAR DISSIPATION IN EXTERIOR DOMAINS

It is proved that the global existence for the nonhomogeneous quasilinear wave equation with a localized weakly nonlinear dissipation in exterior domains.

Existence of viscosity solutions for ~Iessian equations in exterior domains

The Perron method is used to establish the existence of viscosity solutions to the exterior Dirichlet problems for a class of Hessian type equations with prescribed behavior at infinity.

Decay Rates of the Hyperbolic Equation in an Exterior Domain with Half-Linear and Nonlinear Boundary Dissipations

This paper considers the energy decay of the wave equation with variable coefficients in an exterior domain.The damping is put on partly the boundary and partly on the interior of the domain.The energy decay results are established by Riemannian geometry method.

Positive Solutions of a Class of Quasilinear Elliptic Equations in Two-dimensional Exterior Domains

Sufficient conditions for the existence of positive solutions to a class of quasilinear elliptic equations in two-dimensional exterior domains are given.

Rapid Time-Decay Phenomenon of the Incompressible Navier–Stokes Flow in Exterior Domains

This paper focuses on the rapid time-decay phenomenon of the 3 D incompressible NavierStokes flow in exterior domains.By using the representation of the flow in exterior domains,together with the estimates of the Gaussian kernel,the tensor kernel,and the Stokes semigroup,we prove that under the assumption∫0∞∫ΩT[u,p](y,t).νdSydt=0 for the body pressure tensor T[u,p],if u0∈L1(Ω)∩Lσ3(Ω)∩W2/5,5/4(Ω)with‖u0‖3≤ηfor some sufficiently small numberη>0,then rapid time-decay phenomenon of the Navier-Stokes flow appears.If additionally|x|αu0∈Lr0(Ω)for some0<α<1 and 1<r0<(1-α/3)-1 orα=1 and r0=1,then the flow exhibits higher decay rates as t→∞.

Infinitely Many Solutions for an Elliptic Problem with Critical Exponent in Exterior Domain

We consider the following nonlinear problem {-△u=uN＋2/N-2,u〉0 in R^N/Ω,u（x）→0 as｜x｜→＋∞,δu/δn=0 on δΩ,where Ω belong to RN,N ≥ 4 is a smooth and bounded domain and n denotes inward normal vector of δΩ. We prove that the above problem has infinitely many solutions whose energy can be made arbitrarily large when Ω is convex seen from inside （with some symmetries）.

CONTINUOUS DEPENDENCE ON VELOCITY FOR THE BACKWARD DYNAMO EQUATION ON AN EXTERIOR DOMAIN

In this paper we study solutions to a forward Dynamo equation depending continuously on the velocity on an exterior domain,using Logarithmic Convexity Methods.We obtain some more weaker conditions by introducing the unbounded domain.

Blow up for Systems of Wave Equations in Exterior Domain

In this paper the author studies the initial boundary value problem of semilinear wave systems in exterior domain in high dimensions(n ≥ 3). Blow up result is established and what is more, the author gets the upper bound of the lifespan. For this purpose the test function method is used.

BOUNDARY INTEGRAL FORMULAS FOR ELASTIC PLANE PROBLEM OF EXTERIOR CIRCULAR DOMAIN

After the stress function and the normal derivative on the boundary for the plane problem of exterior circular domain are expanded into Laurent series, comparing them with the Laurent series of the complex stress function and making use of some formulas in Fourier series and the convolutions, the boundary integral formula of the stress function is derived further. Then the stress function can be obtained directly by the integration of the stress function and its normal derivative on the boundary. Some examples are given. It shows that the boundary integral formula of the stress function is convenient to be used for solving the elastic plane problem of exterior circular domain.

外区域上Tricomi方程初边值问题解的破裂

该文在n维空间中研究了一类外区域上的非线性Tricomi方程的初边值问题.通过引入适当的泛函并利用Kato引理,得到问题的解会在有限时间内破裂,并给出解的生命跨度的上界估计.

Uniqueness of Positive Radial Solutions for a Class of Semipositone Systems on the Exterior of a Ball

In this paper, we study the positive radial solutions for elliptic systems to the nonlinear BVP: , where Δu = div (∇u) and Δv = div (∇v) are the Laplacian of u, λ is a positive parameter, Ω = {x ∈ Rn : N > 2, |x| > r0, r0 > 0}, let i = [1,2] then Ki :[r0,∞] → (0,∞) is a continuous function such that limr→∞ ki(r) = 0 and is The external natural derivative, and : [0, ∞) → (0, ∞) is a continuous function. We discuss existence and multiplicity results for classes of f with a) fi > 0, b) fi < 0, and c) fi = 0. We base our presence and multiple outcomes via the Sub-solutions method. We also discuss some unique findings.

外区域上非稳恒Navier-Stokes流的加权模估计

该文研究外区域上3维非稳恒Navier-Stokes流的加权模估计.首先构造一个向量场去点乘Navier-Stokes方程的两边,从而将Navier-Stokes流表示为一个积分方程的强解;然后对积分方程的各项进行估计.利用初始条件|x|^(α)u0∈L^(r)(Ω),u_(0)∈L^(σ)^(3)(Ω),其中||u0||3充分小,指数0<α<3,1<r<3且max{r,3/2}<q<∞满足适当的条件,该文推导出加权估计式|||x|^(α)u(t)||_(q)≤C(1+t^(α/2)t^-3/2(q/r-1/q)),其中t>0.在情形0<α≤2下,该文的初始条件要比文献弱,对指数q的限制也比文献宽松.

外部区域上p-Laplace方程的径向对称解

本文讨论R^(N)(N≥2)中外部区域Ω={x∈RN:|x|>r_(0)}上一类p-Laplace边值问题径向对称解的存在性。不同于已有文献,对连续函数f:R→R,不要求f非负,在其满足适当不等式条件下,应用Leray-Schauder不动点定理获得径向对称解的存在性,并在此基础上进一步讨论径向对称解的唯一性。

建筑外墙保温饰面板的环温辐射解耦测试方法

针对环温和辐射耦合测试工况下的建筑外墙保温饰面板,提出一种解耦测试方法。首先,通过信号处理的方法,对饰面板的温度和应变测量信号作S域分析,找到解耦测试信号和耦合测试信号之间的传递函数。其次,通过建立保温饰面板的传热及热应变有限元计算模型,采用数值模拟验证解耦测试方法的准确性。结果表明,温度和应变的耦合与解耦信号高度吻合,应变耦合与解耦信号在非辐射区域较辐射区域延迟大约10 h。

外部区域上半线性椭圆方程的多解

讨论了一个外部区域上的半线性椭圆方程,运用一个Hardy类型的不等式和变分方法,证明了方程存在无限多个解,其中至少有一个是正解.所得结果不同于内部区域的情形.

无穷凹角型区域椭圆边值问题的非重叠区域分解算法

研究无穷凹角型区域椭圆边值问题的一种非重叠型区域分解算法.构造其算法并讨论相应的离散化问题的收敛性,最后给出了数值例子以说明方法的有效性.

域外奇点法分析薄板的弯曲和平面应力问题

本文首先给出了作者推导的两边简支无限长薄板弯曲问题和平面应力问题的基本解，然后运用域外奇点法及给出的基本解分析了一对边简支矩形薄板的弯曲和平面应力问题．计算结果表明，这种方法具有计算量少、精度高等优点。