强迫拟线性波动方程的初值问题

研究具非线性耗散项的强迫拟线性波动方程的初值问题.对初值的C0模不加小性限制,而需其一阶导数的C0模足够小.利用几个关键的先验估计,证明初值问题的整体光滑解的存在性.     

关于“具人工粘性项的2守恒律组的有限差分格式”一文的注记

In [ 2 ], D.Hoff analyzes an implicit finite difference scheme for the mixed initial -value Dirichlet problem for a system of two conservation laws with artif ficial viscosity . The system is a model for isentropic flow in one space dimen-sion .However, in [2], there is an additional condition on the state function p(v),(?)For polytropic gas, p(v) = k²v^-γ, where k>0 and 1<γ≤3,the condition (*) is equivalent to 1<γ<2. In the present note, we remove the restriction(*),so that the main results of [2] still hold for the general state function p(v) with p′(v)<0, p″(v)>0.     

GLOBAL SMOOTH SOLUTIONS FOR SYSTEMS OF GAS DYNAMICS WITH THE DISSIPATION

§1. Introduction The first order quasilinear system arises in several areas of applied mathematics. There has been much investigation to the problem of establishing existence and nonexistence theorems of global smooth solutions for initial value problems to (1.1), (see [1]—[9]). In Nishida's fundamental paper, he assumes that, α is a positive constant, and for a constant δ>0.     

在边界摄动的情况下高阶常微分方程的特征值和特征函数的摄动

小引:数学物理中许多问题都归结为确定微分算子的特征值和特征函数以及将任意函数按特征函数展成级数(或积分)的问题。例如,用富里埃(J.Fourier)方法求偏微分方程满足给定的初始条件与边界条件的解便是如此。近年来,由于量子力学的发展,要求研究微分算子的谱和按微分算子的特征函数展开给定的函数,这一问题一直吸引着人们的极大注意,并且也有很多关于这方面的工作。在文章中作者已研究过关于在边界摄动的情况下,二阶常微分方程的特征值和特征函数的摄动,即     

含多个小参数的高阶常微分方程边值问题的奇摄动

本文研究含多个小参数的高阶线性常微分方程边值问题解的渐近式的构造,导出求渐近解的一般项的迭代过程和有关的余项估计,改进和拓广了[1]的工作。     

Singular perturbation of first boundary value problem for higher order elliptic equations (II)

In this paper we discuss singular perturbations of first boundary value problem for higher order elliptic equations of two parameter and obtain the asymptotic expression for the formal solution containing two-parameter as well as the estimation of its remainder term. These results are the extensions of (2) and (3).     

高阶常微分方程边值问题的奇摄动(Ⅰ)

本文研究当方程和区间的摄动依赖于不同的参数时,高阶常微分方程边值问题解的渐近式的构造.给出求渐近解一般项的递推方程和有关的余项估计.改进和拓广了文[1]和[3]的结果.     

GLOBALLY SMOOTH SOLUTIONS TO CAUCHY PROBLEM OF A QUASILINEAR HYPERBOLIC SYSTEM ARISING IN BIOLOGY

We consider Cauchy problem of the system of nonlinear conservation lawsut -- (liv). = 0, vf -- uz = 0, (x,t) E R x R , (E)with initial datau(2,0) = u0(2), v(x,0) = v0(x), z E R. (I)It has been 8hown in [1,2],the system (E) describes the maro8copic behaviour of some (so-called"chemOtatic ") bacterial populations, which are attracted by the gradient of some chendcalsubstrate, which they metabolize. When the bacteria have depleted the substrate somewliere,this create8 a gradient in the concen…     

具耗散项的绝热气动力学方程组的整体光滑解

考虑拉格朗日坐标下具耗散项的绝热气动力学方程组的初值问题，分别证明了其整体光滑解的存在性与非存在性．     

具非线性耗散项的p-方程组的整体光滑解

研究具非线性耗散项的p-方程组的初值问题.在非线性耗散项较弱的假设条件下,解除了对初值的C1-模的小性限制.即对初值的C0-模不加小性限制,而需其一阶导数的C0-模足够小.运用经典的特征线法和极值原理,分别得到解的C0-模估计和偏导数的C0-模估计.根据光滑解的局部存在性定理和先验估计的结果,利用逐步延拓法,证明初值问题的整体光滑解的唯一存在性.