经典解

本文利用特征线的方法，得到关于拟线性双曲方程组Cauchy问题经典解的一致先验估计.这样的估计给出了系统经典解存在区间的下界。

This paper obtains a uniform a priori estimate of classical solution to the Cauchy problem for quasilinear hyperbolic system by using the method of characteristic , which gives a lower bound on life-span of the classical solution .

利用连续Glimm泛函得到一阶拟线性双曲组具小全变差初值的Cauchy问题经典解的整体存在惟一性，并且给出一个应用举例。

By means of the continuous Glimm functional , the paper obtains the global existence and uniqueness of classical solution to the Cauchy problem for general first order quasilinear hyperbolic systems and an application is given .

一维可压缩Euler方程经典解的破裂

Blowup of Classical Solutions of Compressible Euler Equations in One Space Dimension

Riemann曲面上耗散双曲几何流的整体经典解

Global Classical Solutions to the Dissipative Hyperbolic Geometric Flow on Riemann Surfaces

关于弱非线性、弱涨落的Boltzmann方程链的经典解的存在性问题

Existence of classical solution of the Boltzmann hierarchy for weak nonlinearity and weak fluctuations

初值的导数具有紧支集的对角形双曲组Cauchy问题经典解的整体存在唯一性

Global Classical Solutions to Cauchy Problem of Quasilinear Hyperbolic Systems with Compact-supported Derivative of Initial Data

一类非线性klein－Gorden方程与热传导方程耦合组的Cauchy问题的整体经典解的存在唯一性

Global Existence Theorem of Solution for Cauchy Problem for Nonlinear Heat Equation and klein-Gorden Equation Coupled Systems

半线性热传导方程Cauchy问题全局经典解的存在性与唯一性

The Existence and Uniqueness of the Global Classic Solution to the Cauchy Problem of Semilinear Heat Transfer Equations

一类非线性波动方程和非线性Schrodinger方程耦合组的Cauchy问题的整体经典解

The Global Solution for Cauchy Problem for a Nonlinear Wave Equation and Nonlinear Schrodinger Equation Coupled System

一类非严格双曲型可化约组Cauchy问题的整体经典解

Necessary and sufficient conditions of existence of global smooth solutions for Cauchy problems of a class of non-strictly hyperbolic reducible systems

粘弹性流体力学方程组的整体经典解和不可压缩极限初值的导数具有紧支集的对角形双曲组Cauchy问题经典解的整体存在唯一性

Global Existence and Incompressible Limit for Systems of Viscoelastic Fluids ; Global Classical Solutions to Cauchy Problem of Quasilinear Hyperbolic Systems with Compact-supported Derivative of Initial Data

证明了非线性弹性动力学方程组Cauchy问题经典解的几乎整体存在性，并给出解的生命区间的下界。

We prove the almost global existence of classical solutions to the Cauchy problem for the nonlinear elastodynamic system and give the lower bound of the lifespan of solutions .

以SU（4）规范群为例，提出一个简单求解磁单极子及双子的经典解的方法，它可系统地推广于一般的SU（N）群的情况。

A simple method is proposed to obtain the classical monopole and dyon solutions in the case of SU ( 4 ) symmetry , which can be systematically generalized to the general case of SU ( N ) .

本文采用整体迭代法证明了带小初值的一阶非线性耗散偏微分方程组的Cauchy问题的整体经典解的存在性及指数衰减性质。

By the method of global iteration , this paper proves the existence and exponential decaying property of the global classical solutions to the Cauchy problem of first-order nonlinear damped partial differential equations with small inital data .

借助线性问题的衰减估计，在一适当的Banach空间，利用整体迭代法证明了一类半线性四阶波动方程Cauchy问题整体经典解的存在性。

In this paper , the existence of global classical solutions of Cauchy problems for some semilinear fourth order wave equations are proved by global iterative method , with the help of decay estimates of linear problem in some appropriate Banach space .

给出了n（n>2）维Fourier变换及其性质，并借助它们及Euler积分给出了一类高维热传导方程的Cauchy问题的经典解。

This article gives the transformation of n dimension Fourier and property . With the help of Euler 's integral , it shows a kind of classical explanation of higher dimension equation of heat conduction on Cauchy question , which is n dimension conduction of heat equation .

本文按照Grad~（[6]）指出的方法具体地证明了弱非线性、弱涨落的Boltzmann方程链的经典解的存在性。

An existence and uniqueness theorem for the classical solution to the Boltzmann hierarchy with weak nonlinearity and weak fluctuations is proved by using conventional Boltzmann equation theory in the direction pointed out by H.Grad ~ ( [ 6 ] ) .

此解与以前同类问题的多尺度微扰解不同，在Heisenberg表象中坐标和动量算符的对易关系的简化十分自然，并且量子解能十分方便地过渡到经典解。

In Heisenberg picture the difference from the earlier multiple-scale perturbation solution is that the commutation relation of coordinate and momentum operator is naturally simplified and it is very convenient to get classical result from quantum one in limit condition .

考虑一维均熵流方程组Cauchy问题，验证了文献〔1〕提出的一个开问题的正确性，并且给出了经典解生命跨度精确估计式。

In this paper the authors consider Cauchy problem for the system of one_dimensional isentropic flow , and verify the correctness of open problem put forward by Academician T. T. Li and as a result the estimates of life_span of C 1 solutions are obtained .

构造精确可解格点模型，求其本征能谱、本征态函数和Betheansatz方程等，可为研究超弦的经典解、超对称规范理论与可积体系的关系提供可能工具。

Constructing integrable lattice models and obtaining the eigenstates , energy spectrum and Bethe ansatz equations of the systems may provide a tool for studying classical solutions of string , supersymmetric gauge theory and integrable systems .

证明了Oppenheimer和Snyder关于均匀密度零压星的引力塌缩的经典解是不完整的，它并不能正确地连接作为内解和外解的Friedmann度规和Schwarzschild度规；

The collapse solution of a star with uniform density and zero pressure given in the classic paper of Oppenheimer and Snyder is proved to be incomplete ; it cannot correctly connect the Friedmann and Schwarzschild metrics as the interior and exterior solu tions .

在此基础上，通过RZH解悖标准对语义悖论的经典解悖方案和非经典解悖方案进行衡量、分析与评价，揭示了这些解悖方案的成就与缺陷。

On the basis of this , this dissertation scales , analyzes and values the classical paradox resolution scheme and non-classical paradox resolution scheme by the RZH criterion for paradox resolutions , and reveals the advantages and disadvantages of these paradox resolutions .

一类非线性热传导方程整体经典解的研究

Global Classical Solutions for Nonlinear Heat Conduction Equations of the Same Class

理想磁流体动力学方程组经典解的破裂

Blow-up of classical solutions to the ideal magnetohydrodynamic equations with initial disturbances

对角型拟线性双曲组的整体经典解

Global Classical Solution to Quasi-Linear Hyperbolic System of Diagonal Form

非线性人口发展模型的整体经典解

Global classical solutions to the nonlinear population evolution equation

与时间有关的中子迁移问题的经典解

On the Problems of Neutron Transport Dependent on Time

一类波动方程经典解的生命区间

Life span of the classical solutions to wave equation

一阶拟线性双曲组的经典解对参数的连续依赖性

Continuous Dependence on Parameter of the Classical Solution to First Order Quasilinear Hyperbolic Systems

具耗散项拟线性双曲型方程组典型自由边值问题整体经典解

Global classical solutions to typical free boundary value problem for quasilinear hyperbolic systems with dissipation