Very weak solutions of wave equation for Landau Hamiltonian with irregular electromagnetic field
Very weak solutions of wave equation for Landau Hamiltonian with irregular electromagnetic field
复制标题
不规则电磁场朗道哈密顿量波动方程的极弱解
DOI：
10.1007/s11005-016-0919-6
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发表时间：
2016
影响因子：
1.2
通讯作者：
N. Tokmagambetov
中科院分区：
文献类型：
--
作者：
Michael Ruzhansky;N. Tokmagambetov
在本文中，我们研究朗道哈密顿波动方程的柯西问题，具有与时间相关的不规则（分布）电磁场和类似的不规则速度。对于此类方程，我们描述了“非常弱解”的概念，该概念适用于正则系数存在的解类型。该构造基于考虑系数的 Friedrichs 型缓和器和相应的经典解，以及它们在正则化参数中的定量行为。我们证明，即使对于分布系数，柯西问题也确实有一个非常弱的解，并且在这种解也存在的条件下，这个概念会导致经典或分布型解。
In this paper, we study the Cauchy problem for the Landau Hamiltonian wave equation, with time-dependent irregular (distributional) electromagnetic field and similarly irregular velocity. For such equations, we describe the notion of a ‘very weak solution’ adapted to the type of solutions that exist for regular coefficients. The construction is based on considering Friedrichs-type mollifier of the coefficients and corresponding classical solutions, and their quantitative behaviour in the regularising parameter. We show that even for distributional coefficients, the Cauchy problem does have a very weak solution, and that this notion leads to classical or distributional-type solutions under conditions when such solutions also exist.
影响因子：
2.4
作者：
Claudia Garetto;Michael Ruzhansky
通讯作者：
Claudia Garetto;Michael Ruzhansky
影响因子：
2.5
作者：
Garetto C
通讯作者：
Garetto C