A SUPPLEMENT TO THE PAPERS CONVERGENCE OF THE LAX-FRIEDRICHS SCHEME FOR ISENTROPIC GAS DYNAMICS (Ⅱ)-(Ⅲ)

In the papers (Ⅱ)—(Ⅲ), we studied the global existence of the solutions for the isentropic equation of gas dynamics     

CONVERGENCE OF THE APPROXIMATE SOLUTIONS TO ISENTROPIC GAS DYNAMICS

This paper gives four pairs of entropies (η_i, q_i) (i=1, 2, 3, 4) to the isentropic gas dynamics equations ρ_t+(ρu)_x=0 (ρu)_t+(ρu~2+p(ρ))_x=0 p(ρ)=k~2ρ~γ,1<γ<3。 when all the function equations are satisfied     

THE EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO SYSTEMS OF GAS DYNAMICS WITH A CLASS OF SOURCES

§1. Introduction The existence and asymptotic behavior of solutions are concerned to inhomogeneous system of equations of motions for isentropic viscous fluids:     

DIFFRACTION OF PLANAR SHOCK ALONG COMPRESSIVE CORNER

§0. Introduction Many physicists and numerical analysts have researched the problem in the tittle [1—8]. Four different constructions of solutions have been observed. They are: Regular (RR), Single-Math (SMR), Complex-Mach (CMR) and Double-Mach (DMR) reflexions. The solutions have been being obtained numerically. The transition criteria between different     

OVERTAKING OF SHOCKS OF THE SAME KIND IN THE ISENTROPIC STEADY SUPERSONIC PLANE FLOW

§1. Introduction Courant, Friedrichs and Von Neumann first studied the overtaking of shocks of the same kind in the one-dimensional non-steady and two-dimensional steady adiabatic flow. The results they had obtained are half-experimental and half-analytic. For these results, Hasio and Chang have made strict mathematical     

等熵气体动力学方程组Lax-Friedrichs格式的收敛性(Ⅱ)

许多非线性数学物理方程的研究中,为保证逼近解序列存在一几乎处处收敛的子序列,常运用Helly选取原理。这原理要求函数序列满足如下框架:序列函数本身和它们的全变差一致有界。Oleinik,Conway and Smoller等证明了拟线性单个守恒律方程     

SOME FUNDAMENTAL CONCEPTS ABOUT SYSTEM OF TWO SPATIAL DIMENSIONAL CONSERVATION LAWS

Lax, Gel'fand, Oleinik and others have established some fundamental concepts about system of one spatial dimensional conservation laws, such as hyperbolicity, genuine nonlinearity (convexity), linear degenerate, Rankine-Hugoniot condition, stability condition (entropy condition), stability condition(E) and so on. We extend these concepts to system of two spatial dimension case in this note It is a necessary preliminary for advance study.     

等熵气体动力学方程组Lax-Friedrichs格式的收敛性(Ⅲ)

§1 引言 我们继续考虑满足框架定理~[1]的等熵气体动力学方程组逼近解的收敛性问题,特别是由Lax-Friedrichs格式所诱导的逼近解的收敛性问题。 在文(Ⅱ)中,我们得到了具有绝热指数γ=3/2的方程组(1.1)的Lax-Friedrichs逼近解的收敛性。本文中,对一般的情形1<γ≤5/3(通常气体),我们通过对弱熵的细致分析和参数化测度的正则化研究,建立了Lax-Friedrichs逼近解的收敛性定理。所用的主要技巧是:Euler-Poisson-Darboux方程的分析、分数次微商、Hilbert变换、     

CONVERGENCE OF THE LAX-FRIEDRICHS SCHEME FOR ISENTROPIC GAS DYNAMICS (Ⅲ)

For the general case 1<γ≤5/3, a convergence theorem for the Lax-Friedrichs scheme applied to the isentropic equations of gas dynamics is established. This theorem is true for any approximate solutions satisfying the compactness frame (see [1]) for isentropic gas dynamics (1<γ≤5/3).     

EXISTENCE OF ENTROPY SOLUTIONS TO TWO-DIMENSIONAL STEADY EXOTHERMICALLY REACTING EULER EQUATIONS

We are concerned with the global existence of entropy solutions of the twodimensional steady Euler equations for an ideal gas, which undergoes a one-step exothermic chemical reaction under the Arrhenius-type kinetics. The reaction rate function φ(T) is assumed to have a positive lower bound. We first consider the Cauchy problem(the initial value problem), that is, seek a supersonic downstream reacting flow when the incoming flow is supersonic, and establish the global existence of entropy solutions when the total variation of the initial data is suffciently small. Then we analyze the problem of steady supersonic, exothermically reacting Euler flow past a Lipschitz wedge, generating an additional detonation wave attached to the wedge vertex, which can be then formulated as an initial-boundary value problem. We establish the global existence of entropy solutions containing the additional detonation wave(weak or strong, determined by the wedge angle at the wedge vertex) when the total variation of both the slope of the wedge boundary and the incoming flow is suitably small. The downstream asymptotic behavior of the global solutions is also obtained.