A thermoelastic diffusion theory with microtemperatures and microconcentrations

This article is concerned with a nonlinear theory of thermodynamics for elastic materials in which the particles are subjected to classical displacement, temperature, and mass diffusion fields and whose microelements possess microtemperatures and microconcentrations. The equations of the linear theory are also obtained. It is shown that there exists coupling between temperature, chemical potential, microtemperatures, and microconcentrations even for isotropic bodies. With the help of the semigroup theory of linear operators, we prove the well-posedness of the linear anisotropic problem and we study the asymptotic behavior of the solutions.     

GENERAL CAUCHY PROBLEM FOR THE LINEAR SHALLOW -WATER EQUATIONS ON AN EQUATORIAL BETA-PLANE

1. INTRODUCTION Over the last two decades, studies in the tropical meteorology and ocean have dramatically increased, such as the EI Nino/Southern Oscillation (ENSO), the large-scale heat-induced circulation of the tropical atmosphere and nonlinear effec…     

非线性一维非定常粘性脉动液流问题

本文讨论关于给定压强梯度随时间周期性变化的液压管道粘性脉动流作为一维Ｎ－Ｓ方程的初边值问题的性，并给出其积分形式的解。     

A multimodel approach to stochastic nash games

A decentralized filtering and control scheme is presented for obtaining low-order Nash equilibrium strategies for decision makers using different models of the same large-scale system. Multiparameter singular perturbations are employed to capture the multimodel nature of the fast dynamic subsystems interconnected through slow dynamic variables. The small parameters are appropriately scaled so that the variables in both time scales are well defined. The decision makers have decentralized information structures and are constrained to use only finite dimensional compensators of a specified dimension. It is shown that the proposed scheme is in fact the asymptotic limit of the exact solution as the small parameters go to zero.     

On the Well-posedness of the PWM Control System

One of the basic issues in the study of hybrid systems is the well-posedness (existence and uniqueness of solutions) problem of discontinuous dynamical systems. This paper addresses this problem for a class of piecewise affine discontinuous systems with affine inequalities such as systems with pulse-width modulator under the definition of Carathéodory solutions in terms of an analysis based on lexicographic inequalities and the smooth continuation property of solutions. Furthermore, it is clear that when carrier signal h(t)=0, closed-loop pulse-width modulation (PWM) DC-DC converters are not well posed, and when some condition is satisfied, the closed-loop PWM DC-DC converters with a P controller are well posed. Translated from Acta Automatica Sinica, 2004, 30(1): 37–44 (in Chinese)     

尺度结构的竞争种群系统控制模型的适定性

尺度结构的种群系统控制模型是在年龄结构的种群系统控制模型上发展起来的,近两年,尺度结构得到了越来越多的研究。该文分析了一类基于尺度结构的竞争种群系统模型的适定性问题,利用线性系统比较原理和不动点方法证明了系统解的非负性、有界性、存在唯一性、解对控制变量的连续依赖性。     

连续时间加噪声随机T-S模糊系统的适定性

研究了连续时间加噪声随机T-S模糊系统在Ito^意义下适定性问题，给出了存在惟一性定理的证明．举例说明了相关文献中所使用的加噪声随机T-S模糊系统模型解不具有均方积分意义下适定性，从而有力地说明了Ito^积分在加噪声随机T-S模糊系统模型订义中的重要价值。     

柔性卫星系统的振动自适应边界控制

针对受外部干扰和具有结构参数不确定性的柔性卫星系统,为了抑制其振动和避免控制溢出问题,采用Hamilton变分原理和Euler-Bernoulli梁理论建立了结构无穷维偏微分方程模型,随后基于该无穷维模型设计了带有干扰自适应律的自适应边界控制对柔性卫星振动进行主动控制,并证明了闭环柔性卫星控制系统解的存在性、唯一性和收敛性.最后,仿真结果验证了所设计的自适应边界控制算法的有效性.     

适定性分析在醇酮氧化动力学中的应用

在化工系统DCS先进控制领域和基于机理模型的化工类商品化软件中,大型装置的过程数学模型通常处于核心地位,同时这些场合也对模型的稳定性和动态特性有较高要求。而适定性分析有利于从物理意义和数学的角度分析模型的合理性,并指导正确的数值求解方法,从而产生高质量数学模型。本文结合醇酮氧化过程模拟的实践应用了Lipschitz条件、解的存在唯一性定理、解的延拓、解对初值的连续性和可微性定理和相关常微方程稳定性理论等数学工具,发现了文献中动力学方程组存在的问题,并对其进行了改进与提高；在实际应用中也取得了更好的效果；同时,对于其它类似的数学建模与求解问题也具有理论和实践的参考意义。