流动稳定性弱非线性理论的进一步改进

分析了流动稳定性原弱非线性理论中存在的问题,主要是:(1)解的收敛半径太小;(2)不能处理扰动演化问题,其原因最主要的是处理平均流修正的方法不正确;(3)不能处理一般的初值问题.针对存在的问题,提出了有效的改进办法.其正确性得到数值模拟结果的证实.     

论流动稳定性中的弱非线性理论

弱非线性理论提出已有30多年,被广泛用于流动稳定性及其他领域的问题.但能与实验比较并证实其有效性的理论计算结果很少.本文研究了其原因,发现主要是平均流修正的计算方法有问题,导致它的结果与数值模拟的结果吻合得不好.提出了正确的算法,结果相当满意.     

非中性流动稳定性的弱非线性分析方法

本文分析了非中性流动稳定性的弱非线性理论之困难所在,对适用于中性流动的经典方法进行修正,使之能自然地推广到非中性流动情形.特别,对中性流动,本文方法完全等价于经典渐近分析方法,这是别的一些非中性流动理论所不具备的优点之一.     

对流动稳定性非线性理论中确定幅值演化方程系数的重新考虑*

求解扰动速度幅值的演化规律,是流动稳定性非线性理论的关键问题之一。现有的方法都只能用于准中性的情况,或其中有一定的人为因素。本文将给出解决这一问题新方法。     

圆管内含周期脉动分层流的Floquet稳定性分析

运用线性稳定性理论,结合Floquet理论和Chebyshev配点法对管流内有周期脉动分量的粘性分层流的参数共振现象进行了研究,得到不同流动参数对流场的失稳和参数共振特性的影响．     

C-半群的弱稳定性

引入了C-半群的个体弱稳定性和弱稳定性的概念,给出了弱稳定性的一个充分条件.     

一类三阶非线性微分方程解的不稳定性*

文献[1]讨论了非线性缓变系统的渐近稳定性,文献[2]讨论了三阶变系数线性微分方程解的不稳定性。本文应用文献[1]、[2]的方法讨论一类三阶非线性微分方程解的不稳定性。     

快变海底和自由表面流共振生成的弱非线性Stokes波

运用WKBJ型摄动逼近法,对环境流同沙纹海底共振产生的自由表面水波的非线性效应进行了研究。沙纹海底由缓变平均水深部分和快变海底部分叠加构成。根据对快变海底波长的不同选取,可以相应地激发环境流同非平整海底的同步共振、超谐波共振和次谐波共振,由此产生自由表面波运动。对次谐波共振进行了详细考察。对于定常流自治动力系统,对可能出现的非线性各种稳态及其稳定性进行了探讨。假如环境流具有一个小振动分量,动力系统成为非自治的,则将发生混沌现象。     

非牛顿幂级数流体平面泊肃叶流的非线性稳定性*

非牛顿流体在现代工业生产中,广泛地作为加工的对象,因此非牛顿流体的流动稳定性问题有着重要的生产实际背景。本文选择在聚合物加工时将熔体压入成板口模时形成平面泊肃叶流这一生产背景,研究其非线性稳定性问题,计算其亚临界阈值。     

Further improvement of weakly nonlinear theory of hydrodynamic stability

The problems of the weakly nonlinear theory of hydrodynamic stability has been re-addressed; namely, (i) why is the radius of convergence of its solution too small? (ii) it is not appropriate to use it to deal with the evolution problem of disturbances; the main reason is that the way of calculating the mean flow distortion is inappropriate, (iii) it cannot be used to deal with the initial value problem. Ways of its improvement were proposed. Its correctness was confirmed by its comparison with the results of numerical simulations.     

Periodic Solutions of Porous Medium Equations with Weakly Nonlinear Sources

§ 1.Ｉｎｔｒｏｄｕｃｔｉｏｎ　ＴｈｉｓｐａｐｅｒｉｓｃｏｎｃｅｒｎｅｄｗｉｔｈｔｈｅｔｉｍｅｐｅｒｉｏｄｉｃｓｏｌｕｔｉｏｎｓｏｆｔｈｅｐｏｒｏｕｓｍｅｄｉｕｍｅｑｕａｔｉｏｎｓｗｉｔｈｗｅａｋｌｙｎｏｎｌｉｎｅａｒｓｏｕｒｃｅｓａｎｄｗｉｔｈｔｈｅＤｉｒｉｃｈｌｅｔｂｏｕｎｄａｒｙｖａｌｕｅｃｏｎｄｉｔｉｏｎ ,ｎａｍｅｌｙ ,ｔｈｅｐｒｏｂｌｅｍ ｕ ｔ =Δ(｜ｕ｜ｍ- 1ｕ) +Ｂ(ｘ ,ｔ,ｕ) +ｆ(ｘ ,ｔ)　ｉｎΩ×Ｒ ,(1 .1 )ｕ(ｘ ,ｔ) =0　ｏｎ Ω×Ｒ , (1 .2 )ｕ(ｘ ,ｔ+ω) =ｕ(ｘ ,ｔ)　ｉｎ Ω×Ｒ ,…     

多目标对策的弱Pareto-Nash平衡点集的稳定性研究

通过定义多目标对策的加权Nash平衡点集,得出它和对应对策的弱Pareto-Nash平衡点集之间的关系,证明了在一定条件下的多目标对策的弱Pareto-Nash平衡点集的稳定性.     

Analytic Propagation for Nonlinear Weakly Hyperbolic Systems

The propagation of analyticity for sufficiently smooth solutions to either strictly hyperbolic, or smoothly symmetrizable nonlinear systems, dates back to Lax [14 Lax , P.D. ( 1953 ). Nonlinear hyperbolic equations . Comm. Pure Appl. Math. 6 : 231 – 258 . [Google Scholar]] and Alinhac and Métivier [2 Alinhac , S. , Métivier G. ( 1984 ). Propagation de l'analyticité des solutions de systèmes hyperboliques nonlinéaires [Propagation of analyticity for solutions of nonlinear hyperbolic systems]. Invent. Math. 75, 189–204 . [Google Scholar]]. Here we consider the general case of a system with real, possibly multiple, characteristics, and we ask which regularity should be a priori required of a given solution in order that it enjoys the propagation of analyticity. By using the technique of the quasi-symmetrizer of a hyperbolic matrix, we prove, in the one-dimensional case, the propagation of analyticity for those solutions which are Gevrey functions of order s for some s < m/(m ? 1), m being the maximum multiplicity of the characteristics.     

Derivation of the Hydrodynamic Equations in the Framework of the Bogoliubov Functional Hypothesis

We generalize the Bogoliubov functional hypothesis to the case of multiparticle interaction depending on both the coordinates and momenta of particles. We illustrate this with the examples of two weakly relativistic models: the Darwin model in the theory of charged particles and the Fock model in the general theory of relativity. For these models, based on the chain of the BBGKY equations, we calculate weakly relativistic corrections to the classical transport coefficients and find the conditions under which there is no bijective relation between the parameters of the local equilibrium distribution and the hydrodynamic variables.     

非线性积分微分方程的稳定性

本文研究一类非线性积分微分方程的稳定性问题．给出了简洁、实用的稳定性新准则．文末例子说明了本文结果的优越性。     

非线性半离散森林系统的稳定性

讨论森林发展系统的一类非线性林龄面积结构的半离散模型 ,给出了非线性半离散系统稳定的一些充分条件 .     

Generalized Jacobi Spectral-Galerkin Method for Nonlinear Volterra Integral Equations with Weakly Singular Kernels

We propose a generalized Jacobi spectral-Galerkin method for the nonlinear Volterra integral equations (VIEs) with weakly singular kernels. We establish the existence and uniqueness of the numerical solution, and characterize the convergence of the proposed method under reasonable assumptions on the nonlinearity. We also present numerical results which are consistent with the theoretical predictions.