论文标题
$ 2 \ times 2 $的$ 2 $保护法律的$ bv $解决方案与线性退化字段
Fractional $BV$ solutions for $2\times 2$ systems of conservation laws with a linearly degenerate field
论文作者
论文摘要
$ 2 \ times 2 $非线性双曲线系统具有一个真正的非线性字段和一个线性退化场。证明了分数BV空间中的小初始数据的全球弱解决方案的存在$ bv^s $。指数$ s $与通常的分数Sobolev衍生物有关。 Riemann不变性$ W $和$ Z $分别与真正的非线性组件相对应，并在这项工作中扮演了线性退化组件。我们获得了全球弱解决方案的存在，前提是Riemann坐标$（W_0，Z_0）$在$ BV^S \ Times L^\ Infty $，$ 1/3 \ leq S <1 $中很小。对指数$ s $的限制是由于P.D的基本结果。 Lax，Riemann不变$ Z $在Lax Shock曲线上的变化取决于另一个Riemann不变$ W $的变化。
The class of $2\times 2$ nonlinear hyperbolic systems with one genuinely nonlinear field and one linearly degenerate field are considered. Existence of global weak solutions for small initial data in fractional BV spaces $BV^s$ is proved. The exponent $s$ is related to the usual fractional Sobolev derivative. Riemann invariants $w$ and $z$ corresponding respectively to the genuinely nonlinear component and to the linearly degenerate component play different key roles in this work. We obtain the existence of a global weak solution provided that the initial data written in Riemann coordinates $ (w_0,z_0)$ are small in $ BV^s \times L^\infty $, $1/3 \leq s<1$. The restriction on the exponent $s$ is due to a fundamental result of P.D. Lax, the variation of the Riemann invariant $z$ on the Lax shock curve depends in a cubic way of the variation of the other Riemann invariant $w$.
