非线性波动方程整体解存在的一个必要条件

该文给出了非线性波动方程ｕｎ＝△ｕ＋ｆ（ｕ），（ｆ（ｕ）＝ｕ＾ｐ，ｐ〉１）的Ｃａｕｃｈｙ问题在函数空间Ｃ＾ｋ０（Ｒ＾ｎ）的原点领域有古典整体解的一个必要条件：１／２（ｕ（０）＾２Ｌ２＋ｕｔ（０）＾２Ｌ２）－∫Ｒ＾ｎ∫＾ｕ００ｆ（ｓ）ｄｓｄｘ≤０，并且证明了１〈ｐ〈＾ｎ＾２＋ｎ＋２／ｎ（ｎ－１），ｎ≠１（ｎ＝１，１〈ｐ〈＋∞）古典解与广义解有相同的生命跨度，同时给出了生命跨度的上界估计。     

半参数回归模型非参数分量L1模估计的最优收敛速度

对半参数回归模型，采用分段多项式逼近非参数函数，构造了参数与非参数分量Ｌ１模糊估计，并获得了非参数分量Ｌ１模估计的最优估计收敛速度为Ｏｐ（ｎ＾－ｍ＋ｒ／［２（ｍ＋ｒ）＋１］）。     

Calderon—Zygmund奇异积分算子交换子的L^p有界性

本文证明了当ｂ∈ＢＭＯ时，具有弱核的ＣａｌｄｅｒｏｎＺｙｇｍｕｎｄ奇异积分算子交换（ｂ，Ｔ）ｆ＝ｂＴ（ｆ）－Ｔ（ｂｆ）是Ｌ＾ｐ（１〈ｐ〈∞）有界的，一个等价的命题是双线性算子ｇＴ（ｆ）－ｆＴ（ｇ）∈Ｈ＾１，只要ｆ∈Ｌ＾ｐ，ｇ∈Ｌ＾ｑ，１〈ｐ〈∞，１／ｐ＋１／ｑ＝１。     

Stein流形上θ↑—b的Holder和L^v估计

本文得到了Ｓｔｅｉｎ流形强拟凸域上（ｐ，ｑ）型θ↑－ｂ－方程解的Ｈｏｌｄｅｒ和Ｌ＾ｐ估计。     

关于S^＊p（β）及H^＊p（β）的不等式

设Ｓ＾＊ｐ（β）表示单位圆│Ｚ│〈１内的一族ｐ次对称，正则，单叶，β级星象函数，且Ｈ＾８ｐ（β）表示单位圆不０〈│ｚ│〈１内的一族ｐ次对称，正则，单叶，β级星象函数。本文得到的一些有关函数族Ｓ＾＊ｐ（β）及Ｈ＾＊ｐ（β）的不等式。这些结果都是精确的。     

沿曲线的极大算子和Hilbert变换的L^p有界性

本文沿Ｒ＾ｎ中曲线的极大算子Ｍ和Ｈｉｌｂｅｒｔ变换Ｈ的Ｌ＾ｐ有界性。对一类凸曲线，证明了Ｍ和Ｈ都是Ｌ＾ｐ（Ｒ＾ｎ）上的有界算子，ｐ＞１／     

分数次算子在加权Herz型空间上的有界性

本文证明了具有某种尺寸条件的Ｌ＾ｑ１到Ｌ＾ｑ２有界的分数次次线性算子是Ｋｑ１＾ａ，ｐ（ω１，ω２＾ｑ１）（或Ｋｑ１＾ｑ，ｐ）（ω１，ω２＾ｑ１）到Ｋｑ２＾ａ，ｐ（ω１，ω２＾ｑ２）（或Ｋｑ２＾ａ，ｐ（ω１，ω２＾ｑ２）有界的以及ＨＫｑ１＾ａｐ（ω１，ω２＾ｑ１）（或ＨＫｑ１＾ａｐ（ω１，ω２＾ｑ１）到Ｋｑ２＾ａｐ（ω１，ω２＾ｑ２）（或Ｋｑ２＾ａｐ（ω１，ω２＾ｑ２）有界的。     

初始旋度ω0∈L（logL）^α（α〉1／2）的2—D Euler方程弱解的存在性

本文证明了当初始旋度ω０∈Ｌ（ｌｏｇＬ）＾α∩Ｌ＾α〉１／２时二维无粘Ｅｕｌｅｒ方程柯西问题的整体解的存在性，其中Ｌ（ｌｏｇＬ）＾α是Ｚｙｇｍｕｎｄ函数类，在有界区域，它包含任意的Ｌ＾ｐ∩Ｌ＾１空间。     

关于非齐次细分方程的一个注记

非齐次细分方程在区间上小波构造中用于边界小波的构造,同时它用于向量小波构造等方面,本文讨论了非齐次细分方程在Ｌ＾ｐ（Ｒ）（１≤ｐ≤∞）中解的存在必和正则性,特别地,用迹类算子的谱半径给出了解的Ｓｏｂｌｅｖ指数的一个下界估计,同时命同了一些例子来说明这些一般性的结论     

θ(t)型奇异积分算子的几个有界结果

讨论了θ（ｔ）型奇异积分算子在Ｂａｎａｃｈ值ＬＢ＾ｐ（Ｒ＾ｎ）,（１≤ｐ〈＋∞）空间上的有界性,以及在Ｂａｎａｃｈ值Ｈａｒｂｙ空间Ｈ＾１Ｂ（Ｒ＾ｎ）上的有界性。     

Dissipation and Decay Estimates

We establish the optimal rates of decay estimates of global solutions of some abstract differentialequations,which include many partial differential equations.We provide a general treatment so that any futureproblem will enjoy the decay estimates displayed here as long as the general hypotheses are satisfied.Themain hypotheses are the existence of global solutions of the equations and some growth control of the Fouriertransform of the solutions.We establish the optimal rates of decay of the solutions for initial data in differentspaces.The main ingredients and technical tools are the Fourier splitting method,the iteration skill and theenergy estimates.     

AN IRREGULAR OBLIQUE DERIVATIVE PROBLEM FOR SOME NONLINEAR ELLIPTIC EQUATIONS OF SECOND ORDER

1FormulationofirregularObliqueDerivativeProblemLetDbean(N 1)-connecteddomainwithboundaryr=UU=,r,6Cj(0相似文献   

On the convective Cahn-Hilliard equation with degenerate mobility

In this paper, we study the existence of weak solutions for the convective Cahn-Hilliard equation with degenerate mobility. Based on the Schauder type estimates, we establish the global existence of classical solutions for regularized problems. After establishing some necessary uniform estimates on the approximate solutions, we prove the existence of weak solutions. The nonnegativity and the finite speed of propagation of perturbations of solutions are also discussed.     

On Gaussian decay estimates of solutions to some linear elliptic equations and their applications

In this paper we establish pointwise decay estimates of solutions to some linear elliptic equations by using the Nash–Moser iteration arguments and the ODE method. As applications we obtain sharp Gaussian decay estimates for solutions to nonlinear elliptic equations that are related with self-similar solutions to nonlinear heat equations and standing wave solutions to nonlinear Schrödinger equations with harmonic potential.     

INITIAL-OBLIQUE DERIVATIVE PROBLEMS FOR NONLINEAR PARABOLIC SYSTEMS WITH MEASURABLE COEFFICIENTS

This paper deals with some initial-oblique derivative boundary value problems for nonlinear nondivergent parabolic systems of several second order equations with measurable coefficients in multiply connected domains. Firstly, a priori estimates of solutions for the initial-boundary value problems are given, and then by using the above estimates of solutions and the Leray-Schauder theorem, the existence and uniqueness of solutions for the problems are proved.     

An Upper Estimate of Solution for a General Class of Parabolic Equations

The upper estimates of the functions that satisfy some differential integral inequality are established in this paper. We obtain the uniform estimates of maximum of the solutions for a general class of parabolic equations and extend some known results.     

On Free Boundary Problem for the Non-Newtonian Shear Thickening Fluids

The aim of this paper is to explore the free boundary problem for the NonNewtonian shear thickening fluids. These fluids not only have vacuum, but also have strong nonlinear properties. In this paper, a class of approximate solutions is first constructed, and some uniform estimates are obtained for these approximate solutions. Finally, the existence of free boundary problem solutions is proved by these uniform estimates.     

细菌模型的非协调有限元分析

将非协调元应用于描述细菌传播的反应扩散方程组的初边值问题.借助单元的一些特性和非协调误差估计技巧,分别在半离散和全离散有限元格式下,研究了其数值解与精确解的误差估计,得到了最优的误差估计以及超逼近结果.     

ON GLOBAL EXISTENCE AND NONEXISTENCE FOR SOME NONLINEAR PARABOLIC EQUATIONS

0IntroductionInthispaper,weconsidertheinitial-boundaryvalueproblemforthefailliliarequationwherefiisaboundeddomaininR"withsmoothboulldaryoff,p22isacollstantalldlp(z,u)l5of'(tl" 'forsomea20andc>0.FOrp(x,ti)=Itll"'u,theauthorsofpaper[4,7llolwereillterestedillllollllegativesolutionandhadobtainedfollowillgresults(alsosee[12]).1)If25a 2相似文献   

Boundedness of Solutions for Elliptic Variational Inequalities

Ｂｏｕｎｄｅｄｎｅｓｓ　ｏｆ　Ｓｏｌｕｔｉｏｎｓ　ｆｏｒ　Ｅｌｌｉｐｔｉｃ　Ｖａｒｉａｔｉｏｎａｌ　ＩｎｅｑｕａｌｉｔｉｅｓＢｏｕｎｄｅｄｎｅｓｓｏｆＳｏｌｕｔｉｏｎｓｆｏｒＥｌｌｉｐｔｉｃＶａｒｉａｔｉｏｎａｌＩｎｅｑｕａｌｉｔｉｅｓ￥ＹｅＲｕｉｆ...