论文标题
分析准线性耦合的磁质质量模型：解决方案的溶解度和规律性
Analysis of a quasilinear coupled magneto-quasistatic model: solvability and regularity of solutions
论文作者
论文摘要
我们考虑了由动力学磁化引起的〜quasilinear模型。该模型由麦克斯韦方程的〜磁质质（MQS）近似描述。假设培养基由一个传导和非导电部分组成，那么相对于时间的导数并未完全进入，因此系统可以通过抽象的微分 - 代数方程来描述。此外，通过磁感应，系统与一个方程式结合，该方程沿相关电压沿相关电压的诱导电流，这形成了系统的输入。本文的目的是研究耦合的MQS系统及其解决方案的定期性。因此，我们依赖于希尔伯特空间上的梯度系统的经典理论，并结合了$ \ Mathcal {e} $的概念 - 使用磁能的亚级别。耦合的MQS系统完全符合此一般框架。
We consider a~quasilinear model arising from dynamical magnetization. This model is described by a~magneto-quasistatic (MQS) approximation of Maxwell's equations. Assuming that the medium consists of a~conducting and a~non-conducting part, the derivative with respect to time is not fully entering, whence the system can be described by an abstract differential-algebraic equation. Furthermore, via magnetic induction, the system is coupled with an equation which contains the induced electrical currents along the associated voltages, which form the input of the system. The aim of this paper is to study well-posedness of the coupled MQS system and regularity of its solutions. Thereby, we rely on the classical theory of gradient systems on Hilbert spaces combined with the concept of $\mathcal{E}$-subgradients using in particular the magnetic energy. The coupled MQS system precisely fits into this general framework.
