含分布滞量的非线性双曲偏微分方程组解的振动性

研究了一类具有连续分布时滞变量的非线性双曲型偏微分方程组解的振动性.获得了该方程组在Robin边值条件和Dircichlet边值条件下解振动的充分条件.     

具有连续时滞的中立型双曲偏微分方程系统解的振动性

研究了一类具有连续时滞变量的非线性中立型双曲型偏微分方程系统,解的振动性.获得了该方程组在Robin边值条件和Dirichlet边值条件下解振动的充分条件.     

OSCILLATION OF SOLUTIONS OF THE SYSTEMS OF QUASILINEAR HYPERBOLIC EQUATION UNDER NONLINEAR BOUNDARY CONDITION

Sufficient conditions are obtained for the oscillation of solutions of the systems of quasilinear hyperbolic differential equation with deviating arguments under nonlinear boundary condition.     

Some sufficient conditions for oscillation of impulsive delay hyperbolic systems with Robin boundary conditions

This paper deals with the oscillation problems of delay hyperbolic systems with impulses. Some sufficient conditions for oscillations of impulsive delay hyperbolic systems with Robin boundary conditions are obtained and the criteria of oscillation of the systems are established.     

Oscillations of nonlinear hyperbolic equations with functional arguments via Riccati method

This paper is devoted to the study of the oscillatory behavior of solutions of nonlinear hyperbolic equations with functional arguments by using integral averaging method and a generalized Riccati technique. First, we establish oscillation results for nonlinear hyperbolic equations by applying oscillation criteria for Riccati inequality. Secondly, we present interval oscillation results for nonlinear hyperbolic equations. These results improve and extend oscillation results of Cui and Xu [1].     

Oscillation of Solutions of Neutral Nonlinear Hyperbolic Equations with Doubled Variable Coefficients

In this paper, some sufficient conditions for oscillation of solutions of neutral nonlinear hyperbolic equations with doubled narialbe coefficients are obtained.These results are illustrated by some examples.     

含连续滞量和阻尼项的非线性双曲偏微分方程组的振动性

研究了一类含连续分布滞量和阻尼项的非线性双曲型偏微分方程组运用黎卡提变换获得了该方程组在两类边值条件下解振动的充分条件.     

具高阶Laplace算子的非线性脉冲时滞双曲型方程的振动判据

研究一类具高阶Laplace算子的非线性脉冲时滞双曲型偏微分方程的振动性,利用特征函数法和一阶脉冲时滞微分不等式,获得了该类方程在两类不同边值条件下所有解振动的若干充分性判据.所得结论充分反映了脉冲和时滞在振动中的影响作用.     

非线性时滞双曲型偏泛函微分方程的振动准则

研究一类多滞量非线性双曲型偏泛函微分方程解的振动性,借助广义Riccati变换和微分不等式技巧,获得了该类方程振动的若干新的充分条件,同时也给出了实际应用的例子.     

具非线性扩散系数的中立双曲型偏微分方程系统解的振动定理

考虑一类具非线性扩散系数的中立双曲型偏微分方程系统解的振动性.利用Green公式和Riccati变换,获得了该方程组在两类不同边值条件下振动的若干充分条件.     

里卡蒂方法研究带泛函参数的非线性脉冲时滞双曲方程的振动性

本文研究了带泛函参数的非线性脉冲时滞双曲方程的振动性问题.利用积分平均法和里卡蒂方法得到了这类方程解的振动性的一个充分条件,对非线性时滞双曲方程解的震动性进行了推广,能更好地利用一些现有的脉冲时滞常微分方程解的振动性的结论.     

Zero relaxation and dissipation limits for hyperbolic conservation laws

We are interested in hyperbolic systems of conservation laws with relaxation and dissipation, particularly the zero relaxation limit. Such a limit is of interest in several physical situations, including gas flow near thermo-equilibrium, kinetic theory with small mean free path, and viscoelasticity with vanishing memory. In this article we study hyperbolic systems of two conservation laws with relaxation. For the stable case where the equilibrium speed is subcharacteristic with respect to the frozen speeds, we illustrate for a model in viscoelasticity that no oscillation develops for the nonlinear system in the zero relaxation limit. For the marginally stable case where the equilibrium speed may equal one of the frozen speeds, we show for a model in phase transitions that no oscillation arises when the dissipation is present and goes to zero more slowly than the relaxation. Our analysis includes the construction of suitable entropy pairs to derive energy estimates. We need such energy estimates not only for the compactness properties but also for the deviation from the equilibrium of the solutions for the relaxation systems. The theory of compensated compactness is then applied to study the oscillation in the zero relaxation limit. © 1993 John Wiley & Sons, Inc.     

非线性中立抛物型偏微分方程系统的振动性定理

研究一类非线性中立抛物型时滞偏微分方程系统解的振动性质,利用积分不等式和泛函微分方程的某些结果,获得了该类系统在第一类边值条件下所有解振动的若干充分条件.结论充分表明振动是由时滞量引起的.     

偶数阶非线性中立型偏微分方程系统的振动性

研究一类偶数阶非线性中立型偏泛函微分方程系统解的振动性,利用微分不等式方法和黎卡提变换,获得了该类系统在两类子同边值条件下振动的若干充分条件.     

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.     

Boundary control problems for quasilinear systems of hyperbolic equations

For quasilinear systems of hyperbolic equations, the nonclassical boundary value problem of controlling solutions with the help of boundary conditions is considered. Previously, this problem was extensively studied in the case of the simplest hyperbolic equations, namely, the scalar wave equation and certain linear systems. The corresponding problem formulations and numerical solution algorithms are extended to nonlinear (quasilinear and conservative) systems of hyperbolic equations. Some numerical (grid-characteristic) methods are considered that were previously used to solve the above problems. They include explicit and implicit conservative difference schemes on compact stencils that are linearizations of Godunov’s method. The numerical algorithms and methods are tested as applied to well-known linear examples.     

Existence of chaotic oscillations in second-order linear hyperbolic PDEs with implicit boundary conditions

This paper establishes rigorously mathematical theorems that guarantee the existence of chaotic oscillations in the systems of second-order linear hyperbolic PDEs. It separately considers the systems with nonlinear explicit boundary conditions (EBCs) and nonlinear implicit boundary conditions (IBCs) as well as those with such IBCs subjected to small perturbations, where IBCs include EBCs as special cases but the latter cannot in general be expressed by the former. Numerical examples are demonstrated to illustrate the effectiveness of theoretical results.     

高阶拟线性双曲型方程的精确边界能控性

By means of the existence and uniqueness of semi-global C^1 solution to the mixed initial-boundary value problem with general nonlinear boundary conditions for first order quasilinear hyperbolic systems with zero eigenvalues ,the local exact boundary controllability for higher order quasilinear hyperbolic equations is established.     

Initial boundary value problems for quasilinear symmetric hyperbolic systems with characteristic boundary

This paper is devoted to initial boundary value problems for quasi-linear symmetric hyperbolic systems in a domain with characteristic boundary. It extends the theory on linear symmetric hyperbolic systems established by Friedrichs to the nonlinear case. The concept on regular characteristics and dissipative boundary conditions are given for quasilinear hyperbolic systems. Under some assumptions, an existence theorem for such initial boundary value problems is obtained. The theorem can also be applied to the Euler system of compressible flow. __________ Translated from Chinese Annals of Mathematics, Ser. A, 1982, 3(2): 223–232     

一类脉冲时滞双曲型方程组解的振动性

本文研究含脉冲的时滞双曲型方程组解的振动性,利用二阶脉冲微分不等式的性质,得到了方程组在两类不同边界条件下解振动的一些充分判据.