The r-Hunter-Saxton equation, smooth and singular solutions and their approximation
The r-Hunter-Saxton equation, smooth and singular solutions and their approximation
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r-Hunter-Saxton 方程、光滑解和奇异解及其近似
DOI：
10.1088/1361-6544/abab4d
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发表时间：
2020
期刊：
影响因子：
1.7
通讯作者：
Cotter C
中科院分区：
文献类型：
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作者：
Cotter C
在这项工作中，我们引入了r-Hunter-Saxton方程，它是作为L提出的作用原理的极值出现的Hunter-Saxton方程的推广。我们刻画了柯西问题的解，量化了爆破时间，并研究了各种对称性约化。我们构造了分段线性函数，并证明了它们是r-Hunter-Saxton方程的弱解。
In this work we introduce the r-Hunter–Saxton equation, a generalisation of the Hunter–Saxton equation arising as extremals of an action principle posed in L r. We characterise solutions to the Cauchy problem, quantifying the blow-up time and studying various symmetry reductions. We construct piecewise linear functions and show that they are weak solutions to the r-Hunter–Saxton equation.