arXivDaily arXiv每日学术速递 周一至周五更新
arXiv周末暂无论文更新，休息一下吧，周末愉快~~
arXiv 1105.4640math.AP
收藏

完全非线性2 × 2守恒律组的奇异解

Singular solutions of a fully nonlinear 2x2 system of conservation laws

Henrik Kalisch, Darko Mitrovic

备注：
16 pages, 6 figures, to appear in PEMS
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

讨论了在等离子体研究中产生的非凸严格双曲方程组\pa_t u + \pa_x \big（\Sfrac{u^2+v^2}{2} \big）&=0 \pa_t v + \pa_x（v（u-1））&=0的$δ$ -激波型解的存在性和可容许性.该系统是完全非线性的，即它对于两个变量都是非线性的。后一种系统不承认某些黎曼问题的经典Lax-可采纳解。通过引入复值修正的框架内的弱渐近方法，我们表明，压缩$δ$冲击型解决方案解决了这样的黎曼问题。通过使近似参数为零，修正成为实值，我们得到了一个$δ$型的解决方案的概念。在这个概念的框架下，我们可以证明每一个$2\times 2$守恒律守恒律组都有$δ$型解。

英文摘要：

Existence and admissibility of $δ$-shock type solution is discussed for the following nonconvex strictly hyperbolic system arising in studues of plasmas: \pa_t u + \pa_x \big(\Sfrac{u^2+v^2}{2} \big) &=0 \pa_t v +\pa_x(v(u-1))&=0. The system is fully nonlinear, i.e. it is nonlinear with respect to both variables. The latter system does not admit the classical Lax-admissible solution to certain Riemann problems. By introducing complex valued corrections in the framework of the weak asymptotic method, we show that an compressive $δ$-shock type solution resolves such Riemann problems. By letting the approximation parameter to zero, the corrections become real valued and we obtain a $δ$-type solution concept. In the frame of that concept, we can show that every $2\times 2$ system of conservation laws admits $δ$-type solution.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑