改进的Beam方程Strichartz估计及其应用

从文献[1]中的色散估计出发,以Littlewood-Paley理论为工具,在前人工作的基础上,给出了Beam方程utt+Δ2u+u+h=0的一个改进形式的Strichartz估计。作为应用,借助不动点方法,证明了非聚焦Beam方程在次临界情形的整体适定性。     

Time‐domain Galerkin method for dynamic load identification

This paper proposes a new method called time‐domain Galerkin method (TDGM) for investigating the structural dynamic load identification problems. Firstly, the shape functions are adopted to approximate three parameters, such as the dynamic load, kernel function response, and measured structural response Secondly, defining a residual function could be expressed as the difference of the measured response and the computational response. Thirdly, select an appropriate weighting function to multiply the defined residual function and make integral operation with respect to time to be zero. Finally, when the shape functions are chosen as the weighting function, it establishes the forward model called TDGM. Furthermore, the regularization method could have effectiveness in solving the ill‐posed matrix of load reconstruction and obtaining the accurate identified results of the dynamic load. Compared with the traditional Green kernel function method (GKFM), TDGM can effectively overcome the influences of noise and improve the accuracy of the dynamic load identification. Three numerical examples are provided to demonstrate the correctness and advantages of TDGM. Copyright © 2015 John Wiley & Sons, Ltd.     

一种用墙体反应系数辨识空调负荷的适定方法

本文给出了一种通过实验确定墙体反应系数的的新方法，从理论上分析了该方法适定的必要条件。利用随机试验的模拟方法验证了这种方法的适定性。这为计算空调负荷提供了新的实用基础方法。     

蒸汽发生器一维传热的适定性研究

使用了适定性的数学理论———特征线方法 ,对蒸汽发生器中的一维瞬态两相流传热进行了分析研究 ,目的是为了了解其数学物理本质。根据分析结果 ,蒸汽发生器二次侧的两相流传热是适定的。同时 ,根据这个结果分析得到了求解蒸汽发生器一维传热方程的逆风有限差分格式是稳定的。     

关于允楞水库渗流反演结果适定性解的探讨

渗流问题反演结果往往不是唯一的。结合云南允楞水库实际工程，探讨了反演结果不唯一的原因，并与数值优化方法结合，将反问题转为正问题求解。具体方法为:首先，将坝体渗流计算域分为若干子域，并认为在子域内渗透系数为常数；其次，以钻孔原位压水试验成果为渗流计算初值选取提供依据；最后用三维渗流有限元计算得到的各测孔水位，与实测值进行最优拟合得到反演结果。计算结果表明，该方法简便易行，计算结果精确可靠，可供同类工程的渗流反演分析参考。     

一类变分问题的Galerkin解法

运用Galerkin方法求解数学物理方程，可方便地进行理论分析。文章把一类变分问题转化为等价的Galerkin变分方程，同时运用Lax-Milgram定理证明变分问题解的适定性，并给出Galerkin方法的求解过程和一般公式。     

A multimodel approach to stochastic team problems

This paper develops decentralized team 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 system considered is linear and the cost criterion is quadratic. First, a multimodel solution is obtained when the decision makers make different noisy linear observations of the random initial state only. Then the solution to this static team problem is utilized to obtain a multimodel solution to the dynamic team problem with sampled observations under the one-step-delay observation sharing pattern. In both cases, the well-posedness of the multimodel solution is demonstrated.     

微波生物医学成像算法中的病态及伪逆问题

将微波成像应用于生物医学领域中具有许多潜在应用优势。如同其它物理逆问题 ,下面的两个问题是微波成像计算中常遇到的 :1、是否能得到唯一解 ?2、解是否稳定 ?这两个问题通常称为伪逆和病态问题。它们严重影响了逆问题求解的准确性。文中介绍了微波成像算法的基本原理 ,就伪逆和病态的概念进行了讨论 ,给出了正则化方法等几种可用于求解伪逆和病态问题的方法 ,特别通过举例 ,讨论了这些求解方法的优点和缺点。     

Well‐posedness and numerical performances of the strain gap method

A mixed method of approximation is discussed starting from a suitably modified expression of the Hu‐Washizu variational principle in which the independent fields are displacements, stresses and strain gaps defined as the difference between compatible strains and strain fields. The well‐posedness of the discrete problem is discussed and necessary and sufficient conditions are provided. The analysis of the mixed method reveals that the discrete problem can be split into a reduced problem and in a stress recovery. Accordingly, the discrete stress solution is univocally determined once an interpolating stress subspace is chosen. The enhanced assumed strain method by Simo and Rifai is based on an orthogonality condition between stresses and enhanced strains and coincides with the reduced problem. It is shown that the mixed method is stable and converges. Computational issues in the context of the finite element method are discussed in detail and numerical performances and comparisons are carried out. Copyright © 2001 John Wiley & Sons, Ltd.     

Thermoelastic theory with microtemperatures and dissipative thermodynamics

In this article we derive a nonlinear theory of thermoelastic materials with microtemperatures based on the entropy balance of type III postulated by Green and Naghdi. The work is motivated by an increasing use of materials which possess thermal variation at a microstructure level such that both thermal and microtemperatures waves can propagate with finite speeds and energy dissipation. The equations of the linear theory are also obtained. Then, we use a semigroup approach to derive an existence and uniqueness result for the solutions to the anisotropic problem and to study the asymptotic behavior. Finally, we investigate the impossibility of the localization in time of solutions.