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Analytic Smoothing Effect of the Time Variable for the Spatially Homogeneous Landau Equation

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Journal of Partial Differential Equations 2024年第1期37卷 88-103页

作者： xu chaojiang xu Yan School of Mathematics and Key Laboratory of Mathematical MIIT Nanjing University of Aeronautics and AstronauticsNanjing 210016China.

In this work,we study the Cauchy problem of the spatially homogeneous Landau equation with hard potentials in a close-to-equilibrium *** prove that the solution to the Cauchy problem enjoys the analytic regularizing effect of the time variable with an L^(2)initial datum for positive *** that the smoothing effect of the Cauchy problem for the spatially homogeneous Landau equation with hard potentials is exactly same as heat equation.

关键词： Spatially homogeneous Landau equation analytic smoothing effect hard potentials.

THE ANALYTIC SMOOTHING EFFECT OF LINEAR LANDAU EQUATION WITH SOFT POTENTIALS

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Acta Mathematica Scientia 2023年第6期43卷 2597-2614页

作者：李浩光徐超江 School of Mathematics and Statistics South-Central Minzu UniversityWuhan 430074China Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles MIITNanjing 210016China School of Mathematics and Key Laboratory of Mathematical MIIT Nanjing University of Aeronautics and AstronauticsNanjing 210016China

In this work,we study the linearized Landau equation with soft potentials and show that the smooth solution to the Cauchy problem with initial datum in L^(2)(ℝ^(3))enjoys an analytic regularization effect,and that the... 详细信息

关键词： linear Landau equation analytic smoothing effect soft potential

Dirichlet Problems for the Quasilinear Second Order Subelliptic Equations

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Acta Mathematica Sinica,English Series 1996年第1期12卷 18-32页

作者： xu chaojiang Department of Mathematics Wuhan University Wuhan, 430072 China 武汉大学数学系湖北武汉

In this paper, we study the Dirichlet problems for the following quasilinear secondorder sub-elliptic equation, sum from i,j=1 to m(X~*(A(x,u)xu)+sum from j=1 to m(B(x,u)xu+C(x,u)=0 in Ω, u=φ on Ω,where X={X, …, X} is a system of real smooth vector fields which satisfies the Hrmander’scondition, A(i,j), B, C∈C~∞(■×R) and (A(x, z)) is a positive definite matris. We have provedthe existence and the maximal regularity of solutions in the "non-isotropic" Hlder space associatedwith the system of vector fields X.

关键词： Sub-elliptic equation Dirichlet problem A priori estimate

Initial－boundary　Value　Problem　for　a　Class　of　Quasilinear　Degenerate　Parabolic　Equations

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Wuhan University Journal of Natural Sciences 1996年第2期1卷 179-183页

作者： Nie Lei xu chaojiang

in this work,we study the quasilinear initial-boundary value problem , where is a system of real smooth vector fields which is defined on an open domain M of R'', and satisfies the Hormanderls condition,.Assume that is non characteristic for the system X,,..',Xm. Under some hypothesis for the boundary of domain and the elliptic structure condition for nonlinear coerfficients Aij, Bj, C,(i, j= 1, ..', m), we have proved that the existence and regularity of solution for aboveinitialboudary value problems.

关键词： degenerate parabolic equation vector fields non-isotropic Holder's space initial-boundary value problem

关于Landau方程的Cauchy问题的弱解的唯一性

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中国科学：数学 2021年第6期51卷 899-916页

作者：曹红梅徐超江南京航空航天大学理学院南京211106

本文研究非线性及空间非齐次Landau方程具有一般初值的Cauchy问题,证明在带多项式权的Sobolev空间中的一类弱解的唯一性.

关键词：非齐次Landau方程弱解唯一性

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关于k-Hessian方程解的局部性质

中国科学：数学 2019年第2期49卷 235-248页

作者：王琦田谷基徐超江中南财经政法大学统计与数学学院武汉430073 中国科学院武汉物理与数学研究所武汉430071 武汉大学数学与统计学院武汉430072

本文介绍了k-Hessian算子关于(k-1)-凸可允许解的椭圆性和退化的k-Hessian方程严格凸的局部解.首先分析了k-Hessian算子的椭圆性,特别是(k-1)-凸可允许解的椭圆性.借助对该情形下椭圆性的分析,本文给出了一个k-Hessian算子的分类.利用... 详细信息

本文介绍了k-Hessian算子关于(k-1)-凸可允许解的椭圆性和退化的k-Hessian方程严格凸的局部解.首先分析了k-Hessian算子的椭圆性,特别是(k-1)-凸可允许解的椭圆性.借助对该情形下椭圆性的分析,本文给出了一个k-Hessian算子的分类.利用这个分类,本文构造了退化k-Hessian方程严格凸的局部解.

关键词：局部解椭圆性严格凸性

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关于一类半线性退化椭圆方程的存在性结果

数学进展 1996年第6期25卷 492-499页

作者：徐超江武汉大学数学研究所

本文研究下列半线性退化椭圆Ｄｉｒｉｃｈｌｅｔ问题：这里Ｘ＝｛Ｘ１，…，Ｘｍ｝是一组满足Ｈｏｒｍａｎｄｅｒ条件的实光滑向量场．假设它们在区域的边界附近还满足一些附加条件，以及ｆ∈Ｃ∞〔Ω×Ｒ×Ｒｍ），并且　ｚｆ（ｘ，ｚ... 详细信息

本文研究下列半线性退化椭圆Ｄｉｒｉｃｈｌｅｔ问题：这里Ｘ＝｛Ｘ１，…，Ｘｍ｝是一组满足Ｈｏｒｍａｎｄｅｒ条件的实光滑向量场．假设它们在区域的边界附近还满足一些附加条件，以及ｆ∈Ｃ∞〔Ω×Ｒ×Ｒｍ），并且　ｚｆ（ｘ，ｚ，ξ）≥０，ｓｉｇｎＸｆ（ｘ，ｚ，０）≥μ＞－∞，ｃ（ｘ）≥ｃ０＞０和ｆ（ｘ，ｚ，ξ）关于变量ξ满足一定的增长条件．我们证明了当边界是无穷可微时，上述岸线性Ｄｉｒｉｃｈｌｅｔ问题的光滑解的存在性和唯一性．

关键词：半线性椭圆型方程 Dirichlet问题存在性

Enhancing Thermal and Mechanical Properties of Poly(propylene carbonate) through Composite with Wool Powder

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Enhancing Thermal and Mechanical Properties of Poly(propylen...

GEVREY REGULARITY FOR SOLUTION OF THE SPATIALLY HOMOGENEOUS LANDAU EQUATION

河南省化学会2016年学术年会

作者： chaojiang xu Haibo Chang Fang Zhu Runming Li Hongxia Wang Zhanwei Bu Tong Lin Institute of Environmental and Analytical Science College of Chemistry and Chemical EngineeringHenan University Institute for Frontier Materials Deakin University

Poly(propylene carbonate)(PPC) containing wool powder(WP) was prepared by a simple solution mixing method. The morphological, thermal and mechanical properties of PPC biodegradable composites with different WP content were studied by means of scanning electron microscopy(SEM),Fourier transform infrared(FTIR), differential scanning calorimetry(DSC), thermogravimetric analyses(TGA), static tensile testing and dynamic mechanical analysis. Morphological studies show that WP has good dispersion in PPC matrix when its mass fraction is below 2.0 %. FTIR measurements indicate that strong interactions take place between WP and PPC, which results in increasing the glass transition temperature, thermal decomposition temperature, Young’s modulus, tensile strength and storage modulus of the composites, but decreasing the elongation at break. When the WP content is 2.0 wt%,the composite exhibits the largest improvement in both thermal and mechanical properties.

关键词： wool powder poly(propylene carbonate) composites thermal and mechanical properties

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Acta Mathematica Scientia 2009年第3期29卷 673-686页

作者：陈化李维喜徐超江 School of Mathematics and Statistics Wuhan UniversityWuhan 430072 China Université de Rouen UPRES-A6085 Mathmatiques76821 Mont-Saint-Aignan France

In this paper, we study the Gevrey class regularity for solutions of the spatially homogeneous Landau equations in the hard potential case and the Maxwellian molecules case.

关键词： Landau equation Gevrey regularity smoothness effect