共查询到20条相似文献,搜索用时 281 毫秒
1.
二维带形无界区域中Navier—Stokes方程整体吸引子及其维数估计 总被引:5,自引:0,他引:5
该文讨论二维无界带形区域中Navier-Stokes方程(Ⅰ){ut-△u+uiэuэxi=-△p+f(x,t)∈Ω×R+(1)divu=0(2)u(X,t)∈(H^10(Ω)for t〉0(3)u(x,0)=u0(x)∈H(4)其中Ω=(0,d)×R,d〉0为一常数,u与p为未知量,其中u=(u1,u2)为速度场,p表示压力。我们证明了当u0∈H,f∈V且f「log(e+│x│^2)」^12∈L 相似文献
2.
一类奇异半线性热方程初值问题解 的唯一性结果 总被引:6,自引:0,他引:6
设u(t,x),u(t,x)为初值问题在带形域ST=(0,T)×Rn内的两个非负经曲解,f(x)连续有界非负的实函数,则有如下的结果:(1)若f(x)不恒为零,则在ST中u(t,x);(2)若γ>1,则在ST中u(t,x)u(t,x);(3)若0>γ>1,f(x)0,则问题(1.1),(1.2)的解不唯一且它的所有非平凡解的集合为u(t,s)=这里s≥0是参数,其中记号(γ)+=max{γ,0}. 相似文献
3.
一类非线性偏微分方程组的解具对合重特征的奇性分析 总被引:1,自引:0,他引:1
吴方同 《数学年刊A辑(中文版)》1994,(3)
本文讨论了具有对角线主部一阶非线性偏微分方程组,…=0(i=1,…,m)的解+2的正则性分析.设ρ*∈T*Ω\0,为其线性化算子的对合重特征点,则u(x)在ρ*的奇性将在过ρ*的对合特征流形内传播. 相似文献
4.
本文给出RN(N3)中有界光滑区域Ω上的拟线性椭圆型方程:-∑Ni=1xi·|Du|p-2uxi=λ|u|p-2u+a(x)|u|p-2u+f(x,u),x∈Ω(λ>0,p=Np/(N-p),2p<N)在边界条件:-|Du|p-2Dνu|Ω=ψ(x)|u|q-2u(q=(N-1)p/(N-p))下的多解性结果. 相似文献
5.
一类拟线性椭圆型偏微分方程的先验界的估计 总被引:1,自引:0,他引:1
近几年对边值问题-div(|Du|p-2Du)=λf(u)}在Ω上u|(?)Ω=0正解方面已经得到了许多结果.这里λ>0,Ω是有界区域和对s≥0,f(s)≥0.在本文中在条件N≥p>1,Ω=B1={x∈RN,|x|<1}和f∈C1(0,∞)∩C0([0,∞)),f(0)=0,研究了这类问题的正对称解的先验界估计. 相似文献
6.
积域上的一类粗糙奇异积分算子 总被引:4,自引:0,他引:4
本文讨论了积域Rn×Rm上一类带粗糙核的奇异积分算子Tf(x,y)=p.v.Rn×RmΩ(u,v)|u|n|v|mh(|u|,|v|)f(x-u,y-v)dudv的Lp(Rn×Rm)有界性.这里,Ω为原子Hardy空间H1a(Sn-1×Sm-1)中的函数且h为空间l∞(Lq)(R+×R+)中的径向函数. 相似文献
7.
该文讨论二维无界带形区域中Navier-Stokes方程其中Ω=(0,d)×R,d>0为一常数,u与p为未知量,其中u=(u1,u2)为速度场,p表示压力.我们证明了当u0∈H,f∈V且f[log(e+|x|2)]1/2∈L2(Ω)时,问题(I)在H中存在整体吸引子A,它是的一个子集.对A的Hausdorff维数与Fractal维数我们也给出了估计. 相似文献
8.
带非线性边界条件的非线性抛物型方程组 总被引:1,自引:0,他引:1
本文讨论带非线性边界条件的抛物型方程组ut=Δum,vt=Δvm,x∈Ω,t>0,un=vp,vn=uq,x∈Ω,t>0,u(x,0)=u0(x)δ>0,v(x,0)=v0(x)δ>0,x∈Ω(I)解的整体存在性和在有限时刻爆破问题.其中m,p,q>0,ΩIRN是有界光滑区域,δ>0可以充分小. 相似文献
9.
本文研究积分方程u(x)=λ∫Ωk(x,y)f(y,u(y))dy,λ>0及其它的非线性摄动u(x)=λ∫Ωk(x,y)f(y,u(y))dy+G(u(x)),在k(x,y)非负可测,f(x,u),G(u)满足一定条件下,得到所述方程解的存在唯一性及其迭代逼近. 相似文献
10.
本文在[1]的基础上,证明了Schrodinger型方程tu= (k+ iβ)△u- |u|ρu- λu- g(x), u(x, 0)= u0. 其中k, ρ, λ> 0, x∈Rn 在加权sobolev 空间中指数吸引子的存在性. 相似文献
11.
Petri Juutinen 《NoDEA : Nonlinear Differential Equations and Applications》2010,17(5):601-618
We prove a concavity maximum principle for the viscosity solutions of certain fully nonlinear and singular elliptic and parabolic
partial differential equations. Our results parallel and extend those obtained by Korevaar and Kennington for classical solutions
of quasilinear equations. Applications are given in the case of the singular infinity Laplace operator. 相似文献
12.
The maximum principle is one of the basic characteristic properties of solutions of second order partial differential equations of parabolic (and elliptic) types. The preservation of this property for solutions of corresponding discretized problems is a very natural requirement in reliable and meaningful numerical modelling of various real-life phenomena (heat conduction, air pollution, etc.). In the present paper we analyse a full discretization of a quite general class of linear parabolic equations and present sufficient conditions for the validity of a discrete analogue of the maximum principle in the case when bilinear finite elements are used for discretization in space. 相似文献
13.
Trudinger和Gilbarg—Trudinger对椭园型方程的广义解推广了古典的最大值原理,唯一性定理也有新发展。现在我们把结果推广到一致抛物型方程的第一边值问题。 设Ω是n维欧氏空间E~n中的有界域,Ω为其边界,Q=Ω×(O,T),T是有限值。用(Q)记空间W_2~1(Q)的子空间,其函数在意义下满足如下边界条件: u(x,0)=0,x∈Ω和u(x,t)=0,x∈Ω,t∈(0,T)。 在Q考虑下面形状的方程 相似文献
14.
A Maximum Principle for Elliptic and Parabolic Equations with Oblique Derivative Boundary Problems 下载免费PDF全文
Wang Lihe 《偏微分方程(英文版)》1992,5(4)
This paper prove a maximum principle for viscooity solutions of fully nonlinear, second order, uniformly elliptic and parabolic equations with oblique boundary value conditions. 相似文献
15.
Lothar Collatz 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1958,9(2):118-128
Summary Types of boundary value problems of partial differential equations for infinite domains are discussed which can easily be transformed in such a manner as to allow estimations of error (for approximate solutions) similar to the boundary maximum principle. First, second und third boundary value problems for the outer domain of linear elliptic and certain linear and nonlinear parabolic differential equations are examined. For elliptic differential equations one of the results is that the secound boundary value problem for more than two dimensions can be included. The estimates of the paper can thus be applied to problems of flow around some object, not in the case of two but of three dimensions. This is in a certain sense a counterpart to the conformal mappings method which is successful for two but not for three dimensions. Numerical examples show that estimations of error can easily be carried out. 相似文献
16.
Emil Minchev 《Southeast Asian Bulletin of Mathematics》2002,25(4):681-704
The paper deals with the asymptotic behaviour and global existence of solutions for some classes of nonlinear parabolic equations in regard to the monotone properties of the nonlinear term. The asymptotic behaviour of the solutions of initial-boundary value problem for nonlinear parabolic equations is studied via the method of differential inequalities in order to obtain oscillation criterion for the solutions. Existence of extremal solutions of semilinear elliptic and parabolic equations is investigated via monotone iterative methods. The extremal solutions are obtained via monotone iterates. 相似文献
17.
We prove generalized Aleksandrov–Bakelman–Pucci maximum principles for elliptic and parabolic integro-PDEs of Hamilton–Jacobi–Bellman–Isaacs types, whose PDE parts are either uniformly elliptic or uniformly parabolic. The proofs of these results are based on the classical Aleksandrov–Bakelman–Pucci maximum principles for the elliptic and parabolic PDEs and an iteration procedure using solutions of Pucci extremal equations. We also provide proofs of nonlocal versions of the classical Aleksandrov–Bakelman–Pucci maximum principles for elliptic and parabolic integro-PDEs. 相似文献
18.
We consider positive solutions of elliptic partial differential equations on non-compact domains of Riemannian manifolds. We explicitly determine Martin compactifications and Martin kernels for a wide class of elliptic equations in skew product form by exploiting parabolic Martin kernels for associated parabolic equations. 相似文献
19.
Minoru Murata 《Journal of Functional Analysis》2002,194(1):53-141
We consider positive solutions of elliptic partial differential equations on non-compact domains of Riemannian manifolds. We explicitly determine Martin boundaries and Martin kernels for a class of elliptic equations in skew product form by exploiting and developing perturbation theory for elliptic equations and short/long-time estimates for fundamental solutions of parabolic equations. 相似文献
20.
Hiroaki Aikawa 《Journal d'Analyse Mathématique》2014,124(1):83-116
Harnack’s inequality is one of the most fundamental inequalities for positive harmonic functions and has been extended to positive solutions of general elliptic equations and parabolic equations. This article gives a different generalization; namely, we generalize Harnack chains rather than equations. More precisely, we allow a small exceptional set and yet obtain a similar Harnack inequality. The size of an exceptional set is measured by capacity. The results are new even for classical harmonic functions. Our extended Harnack inequality includes information about the boundary behavior of positive harmonic functions. It yields a boundary Harnack principle for a very nasty domain whose boundary is given locally by the graph of a function with modulus of continuity worse than Hölder continuity. 相似文献