2×2拟线性双曲型守恒律组的粘性消失法(英文)

考虑2×2严格双曲型守恒律组(E),它是在Lax意义下真正非线性的,带有初始条件(Ⅰ)众所周知,在条件(M),(C),(Ⅴ)下,初值问题(E)、(Ⅰ)存在整体光滑解,(参看文[1,2])。然而在文中所采用的方法本质地用来求广义解。本文是用粘性消失法证明文[1]的结果。我们把这个结果看作用粘性消失法求(E)、(Ⅰ)的广义解的第一步。本文也可以看作文[4]的某种推广。在文[4]中,(E)是在Lagrange坐标下均熵气体动力学方程组,但无需条件(Ⅴ)。也是用粘性消失法求得光滑解。     

Global Smooth Solutions for Quasilinear Hyperbolic Equations with "Really Large" Initial Date

Consider the Cauehy problem of the first order quasilinear hyperbolie equations z_t λ(z,w)z_x=0,w_t (z,w)w_x=0, (E) z(0,x)=2_0(x),w(0,x)=w_0(x). (I)We suppose F(z,w)=μ(z,w)-λ(z,w)>O,in D,(1) λ_z(z,w)>O,μ_w(z,w)>O.in D.(2)It is well known that if Q∈∈D (V)where Q≡{(z,w)|z_*≤z≤z~*,w_*≤w≤w~*},z_*=inf z_0(x),~*=8up z_0(x),w_*=infw_0(x),w~*=supw_0(x),then the necessary and 8ufficient COildition for the existence ofglobal smooth solution is[1—3] z_0~＇≥O,w_0~(x)≥0 (M)asz_0(x),w_0(x)∈C~1(R).However,under the COIldition(V),the initial data under     

EXISTENCE AND NONEXISTENCE OF GLOBAL CONTINUOUS SOLUTIONS TO RIEMANN PROBLEM FOR DAMPED P-SYSTEM

In this paper, we extend the result in [16] to general p(v). We prove that, under condition (M) when p≥3/2, where , there exists a unique global continuous solution to the Riemann problem (E), (R), whose structure is similar to the local solution. When 1相似文献   

关于“K类”准线性双曲型守恒律组整体解的研究

<正> 关于准线性双曲型守恒律组整体解的研究,其意义是许多人所熟知的.Diperna R.J.在文[1]中,利用Glimm J.格式证明了“K类”守恒律组之具有界变差初值的初值问题存在整体广义解.关于研究这类方程的意义,该文已经说明. 我们知道,对于方程式的情形,曾经用多种方法研究存在性问题,这不是为了改善证明方法,而是不同方法各自有不同实际意义.但是,迄今对于方程组,用Glimm J.格式几乎成了唯一的方法,其他只有对初值用阶梯函数逼近的方法有一些结果.     

A NOTE ON THE EXISTENCE AND NONEXISTENCE OF GLOBALLY BOUNDED CLASSICAL SOLUTIONS FOR NONISENTROPIC GAS DYNAMICS

Existence of globally bounded classical solution for nonisentropic gas dynamics system has long been studied, especially in the case of polytropic gas. In [4], Liu claimed that sufficient condition has been established. However, the authors find that the argument he used is not true in general. In this article, the authors give a counter example of his argument. Hence, his claim is not valid. The authors believe that it is difficult to impose general conditions on the initial data to obtain globally bounded classical solution.     

EXISTENCE AND NONEXISTENCE OF GLOBAL CONTINUOUS SOLUTIONS OF RIEMANN PROBLEM FOR QUASILINEAR HYPERBOLIC SYSTEMS~(**)

Consider Riemann problem(E),(R)under the condition(M).It is proved that,as0相似文献   

2×2拟线性双曲型守恒律组的粘性消失法

考虑2×2严格双曲型守恒律组(E),它是在Lax意义下真正非线性的,带有初始条件(Ⅰ)众所周知,在条件(M),(C),(Ⅴ)下,初值问题(E)、(Ⅰ)存在整体光滑解,(参看文[1,2])。然而在文中所采用的方法本质地用来求广义解。本文是用粘性消失法证明文[1]的结果。我们把这个结果看作用粘性消失法求(E)、(Ⅰ)的广义解的第一步。本文也可以看作文[4]的某种推广。在文[4]中,(E)是在Lagrange坐标下均熵气体动力学方程组,但无需条件(Ⅴ)。也是用粘性消失法求得光滑解。