基于Nehari等变分法的拟线性方程组多重正解的证明

研究了含有权函数和Hardy-Sobolev临界指标的拟线性方程组,运用Nehari等变分法,证明在一定条件下椭圆方程组正解的存在性以及多重性.     

On Process Model Order Reduction for Controller Design in Discrete Systems

This paper studies the model reduction problem with emphasis on closed loop performance. First, the admissible fixed order models are identified as the ones that are simultaneously stabilizable with the high order process. A complete parametrization of this set in terms of stable parameters that satisfy cubic equality constraints is developed. An optimization problem is then formulated so that its solution identifies the fixed order model that satisfies nominal performance specifications, it is simultaneously stabilizable with the actual process and the actual closed loop optimally satisfies the nominal performance specifications. This nonlinear, infinite dimensional optimization problem is solved by means of exact penalty functions and an asymptotic approximation procedure. An illustrative example is also presented.     

Global Resolvability for Quasilinear Hyperbolic Systems

In this paper, we consider the globally smooth solutions of diagonalizable systems consisted of n-equations. We give a sufficient condition which guarantees the global existence of smooth solutions. Tb.e techniques used in this paper can be applied to study the globally smooth (or continuous) solutions diagonalizable noostrict hyperbolic conversation laws.     

MISO的离散动力系统的最小二乘模型降阶方法

利用最小二乘原理,提出一个基于SVD-Krylov的模型降阶方法,方法兼顾基于SVD模型降阶方法的理论性质和基于Krylov模型降阶方法的有效计算,使得到的降阶系统既能匹配原系统的前r阶模,又能够保持系统的稳定性.利用对称矩阵特征值的极小极大原理,给出了保持系统稳定性的一个新的证明方法,与已有的方法相比,提出的理论证明方法更为简洁.对于离散系统,方法除了能匹配原模型的前r个Markov参数,还可将其推广到任意点处模匹配.数值例子也证明了方法的有效性.     

Equivalence Transformations of Quasilinear First Order Systems and Reduction to Autonomous and Homogeneous Form

Classes of 2×2 first order quasilinear partial differential equations involving arbitrary continuously differentiable functions that can be mapped into autonomous and homogeneous form through equivalence transformations are considered. Equivalence transformations are point transformations of independent and dependent variables of differential equations involving arbitrary elements. The transformations act on the arbitrary elements as point transformations of an augmented space of independent, dependent variables and additional variables representing values taken by the arbitrary elements. Projecting the admitted symmetries into the space determined by the independent and dependent variables, we determine some finite transformations mapping the system into autonomous and homogeneous form. Some physical applications are considered and a comparison with reduction of quasilinear first order systems to autonomous and homogeneous form through Lie point symmetries is discussed.     

Bifurcation in a Quasilinear Variational Problem on a One-Dimensional Manifold

Necessary and sufficient conditions for bifurcation in a variational problem on a one-dimensional closed manifold are obtained. In local coordinates, this problem corresponds to a semilinear 4th-order differential equation and can be regarded as a model equation of problems in the theory of shells. Bibliography: 5 titles.     

一类拟线性系统的Lyapunov不等式

本文研究了一类拟线性系统,引入了反周期边值条件,基于反周期边值条件和数学分析的技巧,建立了新的Lyapunov不等式．     

关于奇摄动拟线性系统

本文目的在于对非线性两点边值问题(1.1)证明其解存在的充分条件。并利用这一结果研究拟线性弱耦合奇摄动系统(DP)q的边界层现象。     

Reflection of Progressing Waves for Quasilinear Hyperbolic Systems

It is proved that when a progressing wave described by conormal distribution for a quasilinear hyperbolic 2 × 2 system hits a solid wall transvenally, the reflected wave remains conormal. In contrast to the semilinear case, such conormal distributions had to be defined inductively to take into account of the fact that the relevant characteristic surfaces are not necessarily smooth. The argument involves a suitable coordinate change to reduce the problem to a simple form and an iterative induction on the tangential regularity of the solution as well as that of the characteristic surfaces at which the wave fronts are situated.     

Aizerman's Problem for Discrete Systems

Absolute stability conditions for nonlinear difference equations are derived. In particular, it is proved that equations with positive Green's functions (impulse responses) satisfy the generalized Aizerman conjecture.     

The Center Manifold Reduction Method for Hopf Bifurcation Theorem

In this paper we apply the center manifold reduction method to prove a Hopf bifurcation theorem for infinite dimensional problem. The asymptolic expression of bifurcation formulae and stability condition are given. The Hopf bifurcation problem for a system of parabolic equations is considered.     

双参数拟线性系统的角层解(英)

本文利用微分不等式的方法研究合双参数的拟线性系统边值问题的角层解，找到了问题的渐近解并对余项作了估计．     

Exact Controllability for Nonautonomous First Order Quasilinear Hyperbolic Systems

By means of the theory on the semi-global C1 solution to the mixed initial-boundary value problem (IBVP) for first order quasilinear hyperbolic systems, we establish the exact controllability for general nonautonomous first order quasilinear hyperbolic systems with general nonlinear boundary conditions.     

Variational Integrators for Thermo-Viscoelastic Discrete Systems

Variational integrators are modern time-integration schemes based on a discretization of the underlying variational principle. In this paper, Hamilton's principle is approximated by an action sum, whose vanishing variation results in discrete Euler-Lagrange equations or, equivalently, in discrete evolution equations for the position and momentum. In order to include the viscous and thermal virtual work (mechanical and thermal virtual dissipation), Hamilton's principle is extended by D'Alembert terms, which account for the time evolution equation of the internal variable and Fourier's law. From this variational formulation, variational integrators using different orders of approximation of the state variables as well as of the quadrature of the action integral are constructed and compared. A thermo-viscoelastic double pendulum comprised of two discrete masses connected by generalized Maxwell elements, and subject to heat conduction between them serves as a discrete model problem. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Cauchy Problem for General Rst Order Inhomogeneous Quasilinear Hyperbolic Systems

In this paper, we consider Cauchy problem for general first order inho- mogeneous quasilinear strictly hyperbolic systems. Under the matching condition, we first give an estimate on inhomogeneous terms. By this estimate, we obtain the asymptotic behaviour for the life-span of C¹ solutions with “slowly” decaying and small initial data and prove that the formation of singularity is due to the envelope of characteristics of the same family.     

Existence and Asymptotic Behavior of Solutions for Quasilinear Parabolic Systems

This paper is concerned with the existence, uniqueness and asymptotic behavior of solutions for the quasilinear parabolic systems with mixed quasimonotone reaction functions endowed with Dirichlet boundary condition, in which the elliptic operators are allowed to be degenerate. By the method of the coupled upper and lower solutions and its monotone iterations, it is shown that a pair of coupled upper and lower solutions ensures that the unique positive solution exists and is globally stable if the quasisolutions are equal. Moreover, we study the asymptotic behavior of solutions to the Lotka-Volterra predator-prey model with the density-dependent diffusion.     

对角型拟线性双曲组的整体经典解

本文在特征值部分线性退化、部分弱线性退化时,考察一阶拟线性对角型严格双曲组的柯西问题,当初值满足适当的条件时得到了其整体经典解的存在性.