空间均匀Boltzmann方程的唯一性

本文讨论空间均匀的Boltzmann方程的唯一性.当碰撞核满足Grad假设且对某s>2初始值f0∈Ls1(R3) ∩L1logL1时,我们证明了该方程守恒解是唯一的.     

Boltzmann and Fokker–Planck Equations Modelling the Elo Rating System with Learning Effects

Journal of Nonlinear Science - In this paper, we propose and study a new kinetic rating model for a large number of players, which is motivated by the well-known Elo rating system. Each player is...     

Decay and stability of solutions to the Fokker–Planck–Boltzmann equation in

In this paper, we use the method of constructing the compensating function introduced by Kawashima and the standard energy method to study the global existence of solutions to the Fokker–Planck–Boltzmann equation in the whole space. The time decay and uniform stability of solutions to the global Maxwellian are also obtained.     

空间齐次的Fokker-Planck-Boltzmann方程

本文讨论如下空间齐次的Fokker Planck Boltzmann方程 : f t-νΔξf=Q(f,f) ,f( ξ ,0 ) =f0 ( ξ) ,这里Q(f,f)是Boltzmann碰撞算子 .在角截断的硬位势情况下 ,我们利用算子半群理论和紧性方法证明了当初始值属于L12 时该方程古典解的整体存在性 ,并且建立了能量线性增长关系式 .     

Boltzmann方程的两个解的平均作为二粒子Boltzmann方程系的解

在这篇文章,由Boltzmann方程的两个解构造出二粒子Boltzmann方程系的一类解。利用这个结果,求出了二粒子Boltzmann方程系的平衡解及宏观运动方程组。     

Boltzmann方程的L~1稳定性

本文研究在小初值情况下Boltzmann方程经典解的L1稳定性.借助于Toscani等人所给的估计,对硬位势和软位势作了讨论,完善了[2]中关于硬球模型的结果.     

复Monge—Ampere方程的特征值问题

讨论了复空间中强拟凸域上的复Ｍｏｎｇｅ－Ａｍｐｅｒｅ方程的特征值问题，证明了特征值问题解的存在唯一性，并给出了这个特征值与一类复空间中复Ｌａｐｌａｃｅ算子的第一特征值的关系，最后利用特征值及特征函数的存在性讨论了一类复Ｍｏｎｇｅ－Ａｍｐｅｒｅ方程的解的存在性及其分岐。     

一类Boltzmann方程的临界解

以多种应用为背景的Boltzmann方程,其临界解的讨论已有许多结果,例如,具齐次边界条件的柱模型,具广义反射边界条件的球模型,对于平板模型,有广义反射边界条件和积分边界条件的讨论,但都局限于有限板的情形。对于无限介质的平板模型,G.C.Pomraning讨论了如下特殊的临界间题:     

Smoothness of the Solution of the Spatially Homogeneous Boltzmann Equation without Cutoff

Abstract

For regularized hard potentials cross sections, the solution of the spatially homogeneous Boltzmann equation without angular cutoff lies in Schwartz's space 𝒮(? ^N ) for all (strictly positive) time. The proof is presented in full detail for the two-dimensional case, and for a moderate singularity of the cross section. Then we present those parts of the proof for the general case, where the dimension, or the strength of the singularity play an essential role.     

一类函数方程C~2解的唯一性

讨论了一类迭代方程的唯一性 ,对文 [1 ]中关于唯一性的猜测给出了肯定的解答     

Probability Approaches to Spatially Homogeneous Boltzmann Equations

Abstract

This article is devoted to the study of the probability measure solutions to the spatially homogeneous Boltzmann equations. First, we provide a measure theoretical treatment to the Boltzmann collision operator. Then, the existence results both for the cutoff kernels and the non cutoff ones are established in the sense of measure-valued solutions. We also give a partial uniqueness result and some estimates for pth order moment (p > 2).     

The Spatially Homogeneous Relativistic Boltzmann Equation with a Hard Potential

In this paper, we study spatially homogeneous solutions of the Boltzmann equation in special relativity and in Robertson-Walker spacetimes. We obtain an analogue of the Povzner inequality in the relativistic case and use it to prove global existence theorems. We show that global solutions exist for a certain class of collision cross sections of the hard potential type in Minkowski space and in spatially flat Robertson-Walker spacetimes.     

关于Boltzmann方程的空间均匀的ES模型

在Prandtl数Pr∈[2/3,∞)的情况下,我们讨论了Boltzmann方程的空间均匀的椭圆统计模型.首先,我们建立了解的存在唯一性.其次,我们证明了该解收敛到平衡态并给出了其Maxwell分布型的下界估计.最后,我们给出了熵等式从而证明了该方程的熵是衰减的.     

半线性双调和方程解的存在性

考虑了有界光滑区域ΩR~d,d=2,3上的一类半线性双调和方程.非线性项φ（｜▽u｜）是由｜▽u｜~p产生的.应用Schaefer不动点定理证明了当d=2（或d=3）,p满足2≤p〈∞（或2≤p≤6）时,该问题的解是存在的,并且解是局部唯一的.     

The Uniqueness of Steady-state Solution for Two-phase Continuous Casting Problem

Concerning steady-state continuous casting problem, we know that if the number of phases is one, both existence and uniqueness had been solved ([1], [2], [3]), if the number of phases is two, the existence had been proved ([4]), but the uniqueness of weak solution is an open problem all the time. This paper is devoted to solving this problem.     

空间齐次推广的耗散碰撞Bootzmann方程的Cauchy问题(英文)

关于一类空间齐次推广的耗散碰撞Boltzmann方程Cauchy问题 ,对于一般的初始条件得到了正古典解的存在唯一性 .     

Regularity - Properties of the Solution of the Homogeneous Wave Equation

The aim of this paper is to prove regularity-properties for solutions of the wave equation in B with p < 1. Up to now no such result is known. For p ≥ 1 a large amount of work has been done, cf. for instance [9], [7], [8], [10]. The results in this paper for p> 1 are not optimal, which can be seen comparing them with [9]. Whether or not our results are optimal for p ≤ 1 is open.