相互作用的Brinkman-Forchheimer方程组与Darcy方程组的结构稳定性

研究了在R³中有界区域内的多孔介质中相互作用的Brinkman-Forchheimer流体与Darcy流体方程组解的结构稳定性,假设在Ω₁中流体速度较慢,满足BrinkmanForchheimer方程组,而在Ω₂中,饱和流体满足Darcy方程组.借助于温度的四阶范数估计以及Sobolev不等式,构造能量表达式,推出该表达式所满足的微分不等式,积分得到了相互作用Brinkman-Forchheimer与Darcy流体方程组的解对Brinkman系数的连续依赖性结果.     

一维弱噪声随机Burgers方程的奇摄动解

讨论了一类有界区域上具有有色噪声干扰的随机Burgers方程奇摄动解,其波动率服从弱噪声Ornstein-Uhlenbeck(O-U)过程.由波运动的转移概率密度函数满足的后向Kolmogorov方程,得到随机Burgers的期望所满足的后向Kolmogorov方程.由于期望满足的后向Kolmogorov方程的初边值问题条件涉及到一类确定性Burgers方程的解,因此该问题实际上是Burgers方程和Kolmogorov方程的联立形式.首先,应用奇摄动方法,对一类确定性Burgers方程进行了正则渐近展开,由Schauder估计、Ascoli-Arzela定理证明了非线性抛物方程渐近解的有界性与存在性,由Lax-Milgram定理证明了线性抛物方程渐近解的有界性与存在性,得到波速率的形式渐近解.其次,由奇摄动理论,对期望满足的方程进行了奇摄动渐近展开和边界层矫正,由二阶线性偏微分方程理论,得到边界层函数渐近解存在且有界.应用极值原理、De-Giorgi迭代技术分别证明了波速率和波期望渐近解的余项有界,得到渐近解的一致有效性.     

一类含临界耦合非线性项的奇异椭圆方程组的正解

本文研究了一类含临界指数与耦合非线性项的奇异椭圆方程组. 利用变分方法与极大值原理, 通过证明对应的能量泛函满足局部的 (PS)c 条件, 得到了这类方程组正解的存在性, 推广了单个方程与方程组中的相应结果.     

正规升列在参数代数方程组求解中的应用

本文提出一种利用多项式系统的正规零点分解的算法来求解代数方程组以及带有参数的代数方程组的方法．对于给定的的代数方城组,通过正规分解,可以得到一组具有三角形式的分解．根据这种三角形式,我们可以给出代数方程组的所有解．而对于带有参数方程组,将给出方程组有解时参数需满足的条件．进一步,对于给定的参数值,正规分解中得到三角形式仍然保持,通过求解三角形式的方程组从而得出原参数方程组的解．     

一类病毒与抗体的反应扩散方程组解的性质

对一类病毒与抗体的反应扩散方程组利用变量变换的方法得到与其具有同解性的反应扩散方程.在一定假设条件下,研究此方程解的一些性质,再由紧性得到满足原假设的解的收敛序列,从而得到此方程解的存在性、惟一性与收敛性.借助于方程与方程组的同解性,最终得到了反应扩散方程组解的性质.     

一类铁磁链型方程组的Cauchy问题

本文考虑一类推广的铁磁链型方程组的Cauchy问题的整体可解性,以及当t→∞时解的渐近性质.     

多维铁磁链型方程组

本文考虑一类推广的多维铁磁链型方程组的齐次边值问题的整体可解性.     

环形空腔内自然对流问题的Galerkin方法

本文讨论了环形空腔内自然对流问题所满足的Boussinesq方程组——关于涡度ζ、流函数φ及温度θ的椭圆-抛物非线性耦合方程组 用Galerkin方法对其进行了数值分析,得到了Galerkin逼近(含半离散和全离散)的最优先验误差估计。     

一类抽象算子方程组的迭代解及其应用

在Banach空间中, 利用半序方法讨论了一类抽象算子方程组解的存在唯一性, 推广和统一了以前的一些结果. 然后应用到 Banach 空间非线性积分方程组, 得到了方程组的唯一解, 构造了收敛于方程组唯一解的迭代序列并给出了相应的误差估计.     

多孔介质中的B rinkman-Forchheimer模型的收敛性

本文研究Brinkman-Forchheimer方程组的结构稳定性.首先我们得到一些有用的先验界,然后在此基础上推出解所满足的微分不等式,最后建立了解对Brinkman系数v的收敛性结果.     

THE CONSTRUCTION OF DENUMERABLE q-PROCESSES IN RANDOM ENVIRONMENTS SATISFYING (F) OR (B)

This article is a continuation of [9]. Based on the discussion of random Kol-mogorov forward (backward) equations, for any given q-matrix in random environment,Q(θ) = (q(θ; x, y), x, y ∈ X), an infinite class of q-processes in random environments sat-isfying the random Kolmogorov forward (backward) equation is constructed. Moreover,under some conditions, all the q-processes in random environments satisfying the random Kolmogorov forward (backward) equation are constructed.     

Nonlinear Transformations of Evolution Families Generated by Diffusion Processes

We derive closed equations for some nonlinear transformations of solutions to forward and backward Kolmogorov equations (which are parabolic equations with respect to measures and functions). In particular, we obtain closed equations for the logarithmic derivatives of smooth diffusion measures and for the Radon–Nikodym derivatives of a pair of absolutely continuous diffusion measures. Similar results are obtained for the backward Kolmogorov equation. Bibliography: 14 titles.     

THE CONSTRUCTION OF DENUMERABLE q-PROCESSES IN RANDOM ENVIRONMENTS SATISFYING （F） OR （B）

This article is a continuation of[9].Based on the discussion of random Kolmogorov forward（backward）equations,for any given q-matrix in random environment, Q（θ）=（q（θ;x,y）,x,y∈X）,an infinite class of q-processes in random environments satisfying the random Kolmogorov forward（backward）equation is constructed.Moreover, under some conditions,all the q-processes in random environments satisfying the random Kolmogorov forward（backward）equation are constructed.     

On solutions of Kolmogorovʼs equations for nonhomogeneous jump Markov processes

This paper studies three ways to construct a nonhomogeneous jump Markov process: (i) via a compensator of the random measure of a multivariate point process, (ii) as a minimal solution of the backward Kolmogorov equation, and (iii) as a minimal solution of the forward Kolmogorov equation. The main conclusion of this paper is that, for a given measurable transition intensity, commonly called a Q-function, all these constructions define the same transition function. If this transition function is regular, that is, the probability of accumulation of jumps is zero, then this transition function is the unique solution of the backward and forward Kolmogorov equations. For continuous Q-functions, Kolmogorov equations were studied in Feller?s seminal paper. In particular, this paper extends Feller?s results for continuous Q-functions to measurable Q-functions and provides additional results.     

Carleman estimates for stochastic parabolic equations with Neumann boundary conditions and applications

By a dual method, two Carleman estimates for forward and backward stochastic parabolic equations with Neumann boundary conditions are established. Then they are used to study a null controllability problem and a state observation problem for some stochastic forward parabolic equations with Neumann boundary conditions.     

Backward stochastic Volterra integral equations—Representation of adapted solutions

For backward stochastic Volterra integral equations (BSVIEs, for short), under some mild conditions, the so-called adapted solutions or adapted M-solutions uniquely exist. However, satisfactory regularity of the solutions is difficult to obtain in general. Inspired by the decoupling idea of forward–backward stochastic differential equations, in this paper, for a class of BSVIEs, a representation of adapted M-solutions is established by means of the so-called representation partial differential equations and (forward) stochastic differential equations. Well-posedness of the representation partial differential equations are also proved in certain sense.     

Dynamic Evasion-Interrogation Games with Uncertainty in the Context of Electromagetics

We consider two player electromagnetic evasion-pursuit games where each player must incorporate significant uncertainty into their design strategies to disguise their intension and confuse their opponent.In this paper,the evader is allowed to make dynamic changes to his strategies in response to the dynamic input with uncertainty from the interrogator.The problem is formulated in two different ways; one is based on the evolution of the probability density function of the intensity of reflected signal and leads to a controlled forward Kolmogorov or Fokker-Planck equation.The other formulation is based on the evolution of expected value of the intensity of reflected signal and leads to controlled backward Kolmogorov equations.In addition,a number of numerical results are presented to illustrate the usefulness of the proposed approach in exploring problems of control in a general dynamic game setting.     

Dynamic Evasion-Interrogation Games with Uncertainty in the Context of Electromagnetics

We consider two player electromagnetic evasion-pursuit games where each player must incorporate significant uncertainty into their design strategies to disguise their intension and confuse their opponent. In this paper, the evader is allowed to make dynamic changes to his strategies in response to the dynamic input with uncertainty from the interrogator. The problem is formulated in two different ways. One is based on the evolution of the probability density function of the intensity of reflected signal and leads to a controlled forward Kolmogorov or Fokker-Planck equation. The other formulation is based on the evolution of expected value of the intensity of reflected signal and leads to controlled backward Kolmogorov equations. In addition, a number of numerical results are presented to illustrate the usefulness of the proposed approach in exploring problems of control in a general dynamic game setting.     

Differentiability of Backward Stochastic Differential Equations in Hilbert Spaces with Monotone Generators

The aim of the present paper is to study the regularity properties of the solution of a backward stochastic differential equation with a monotone generator in infinite dimension. We show some applications to the nonlinear Kolmogorov equation and to stochastic optimal control.     

关于拟线性混合型边界问题的概率表示

关于某些抛物型和椭圆型偏微分方程的混合边界问题的解被表示为一类联系于Ito正向反射边界随机微分方程的反向随机微分方程的解.