Weakly singular shock profiles for a non-dispersive regularization of shallow-water equations
Weakly singular shock profiles for a non-dispersive regularization of shallow-water equations
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DOI：
10.4310/cms.2018.v16.n5.a9
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发表时间：
2018-05
期刊：
影响因子：
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通讯作者：
Yue Pu;R. Pego;D. Dutykh;D. Clamond
中科院分区：
文献类型：
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作者：
Yue Pu;R. Pego;D. Dutykh;D. Clamond
我们研究了最近由D. Clamond和D. Dutykh （common）引入的经典Saint-Venant（浅水）方程的正则化。Nonl。科学。号码。仿真。55(2018)237-247)。这种正则化是非色散的，形式上守恒质量、动量和能量。我们证明了对于每一个经典激波，系统都有一个相应的非振荡行波解，它是连续的和分段光滑的，在一个点上有一个弱奇点，在这个点上能量像经典激波一样耗散。该系统还允许尖角孤立波的上升和下降。
We study a regularization of the classical Saint-Venant (shallow-water) equations, recently introduced by D. Clamond and D. Dutykh (Commun. Nonl. Sci. Numer. Simulat. 55 (2018) 237-247). This regularization is non-dispersive and formally conserves mass, momentum and energy. We show that for every classical shock wave, the system admits a corresponding non-oscillatory traveling wave solution which is continuous and piecewise smooth, having a weak singularity at a single point where energy is dissipated as it is for the classical shock. The system also admits cusped solitary waves of both elevation and depression.