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.     

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…     

SOME RESULTS ON HYPERBOLIC SYSTEMS WITH RELAXATION

In this article, first, the authors prove that there exists a unique global smooth solution for the Cauthy problem to the hyperbolic conservation laws systems with relaxation; second, in the large time station, they prove that the global smooth solutions of the hyperbolic conservation laws systems with relaxation converge to rarefaction waves solution at a determined L^P（p ≥ 2） decay rate.     

SINGULAR PERTURBATION OF FIRST BOUNDARY VALUE PROBLEM FOR HIGHER ORDER ELLIPTIC EQUATIONS(Ⅱ)

In this paper we discuss singular perturbations offirst boundary value problem for higher order ellipticequations of two parameter and obtain the asymptoticexpression for the formal solution containing two-parameter as well as the estimation of its remainderterm.These results are the extensions of(2)and(3).     

VACUUM PROBLEM FOR THE DAMPED p-SYSTEM

ＶＡＣＵＵＭＰＲＯＢＬＥＭＦＯＲＴＨＥＤＡＭＰＥＤｐ－ＳＹＳＴＥＭＺｈｅｎｇＹｏｎｇｓｈｕ（郑永树）（Ｄｅｐｔ．ｏｆＡｐｐｌ．Ｍａｔｈ．，ＨｕａｑｉａｏＵｎｉｕｅｒｓｉｔｙ，Ｑｕａｎｚｈｏｕ，３６２０１１，Ｃｈｉｎａ．）Ａｂｓｔｒａｃｔ：Ｔｈｅａｕｔ...     

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．     

高阶椭圆型方程第一边值问题的奇摄动(Ⅱ)

本文研究含双参数的高阶椭圆型方程第一边值问题的奇摄动,得到包含两个形式参数的渐近解表达式,并对余项进行估计,拓广了文[2]、[3]的结果.     

关于Dafermos折线逼近法的注记

The remark in [1] shows that the polygonal approximations suggests the numerical method of construction of a solution of the initial value problem of a conservation law for piecewise linear f(u) and u₀(x) a step function. Unfortunately, there is no guarantee that one can reach by this procedure every point t∈[0,∞) in a finite number of steps. In the present note, we give this guarantee.