论文标题
熵弱解决方案的一般性持续性，用于双曲线保护法系统
Generalized persistence of entropy weak solutions for system of hyperbolic conservation laws
论文作者
论文摘要
令$ u（t，x）$成为解决一个空间维度标量保护法的解决方案。众所周知，即使为了平滑的初始数据，解决方案在有限的时间内也会变得不连续，而全局熵弱解决方案也可以最好地存在于界面总变化的空间中。解决方案属于$ h^1 $是不可能的，因为Sobolev嵌入定理$ h^1 $函数是h $ \ mathrm {\ ddot {o}} $ lder连续。但是，我们注意到，从任何点$（t，x）$，我们可以向下绘制一个广义的特征，该特征在$ y =α（t，x）$下符合初始轴。如果我们将$ u $视为$（t，y）$的函数，则如果初始数据属于$ h^1 $，则确实属于$ h^1 $作为$ y $的函数。我们可以称这种熵弱解决方案的普遍持久性（高规律性）。本文的主要目的是证明标量的某种广义持久性（高规律性）和$ 2 \ times 2 $在一个空间维度中的双曲线保护法的寺庙系统。
Let $u(t,x)$ be the solution to the Cauchy problem of a scalar conservation law in one space dimension. It is well known that even for smooth initial data the solution can become discontinuous in finite time and global entropy weak solution can best lie in the space of bounded total variations. It is impossible that the solutions belong to ,for example ,$H^1$ because by Sobolev embedding theorem $H^1$ functions are H$\mathrm{\ddot{o}}$lder continuous. However, we note that from any point $(t,x)$ we can draw a generalized characteristic downward which meets the initial axis at $y=α(t,x)$. if we regard $u$ as a function of $(t,y)$, it indeed belongs to $H^1$ as a function of $y$ if the initial data belongs to $H^1$. We may call this generalized persistence (of high regularity) of the entropy weak solutions. The main purpose of this paper is to prove some kinds of generalized persistence (of high regularity) for the scalar and $2\times 2$ Temple system of hyperbolic conservation laws in one space dimension .
