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arXiv 1202.2989nlin.CDmath.APmath.DSphysics.flu-dyn
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一种shock wave混沌模型

A model for shock wave chaos

Aslan Kasimov, Luiz Faria, Rodolfo R. Rosales

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4 pages, 4 figures
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摘要：

我们提出了以下模型方程：预测混沌冲击波的\[u_{t}+1/2(u^{2}-uu_{s})_{x}=f(x,u_{s}), \]。它是在半线$x<0$上给出的，对于任何$t\ge0$，激波都位于$x=0$上。这里$u_{s}(t)$是激波状态，源项$f$被假设满足正文中解释的某些可积性约束。我们证明，这个简单的方程再现了许多属性的爆炸气体混合物中，其中一个发现通过解决反应欧拉方程：存在稳定的行波解和它们的不稳定性，级联的倍周期分叉，发病的混乱，和冲击波形成的反应区。

英文摘要：

We propose the following model equation: \[u_{t}+1/2(u^{2}-uu_{s})_{x}=f(x,u_{s}), \] that predicts chaotic shock waves. It is given on the half-line $x<0$ and the shock is located at $x=0$ for any $t\ge0$. Here $u_{s}(t)$ is the shock state and the source term $f$ is assumed to satisfy certain integrability constraints as explained in the main text. We demonstrate that this simple equation reproduces many of the properties of detonations in gaseous mixtures, which one finds by solving the reactive Euler equations: existence of steady traveling-wave solutions and their instability, a cascade of period-doubling bifurcations, onset of chaos, and shock formation in the reaction zone.

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。

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