Analysis of a quasilinear coupled magneto-quasistatic model: solvability and regularity of solutions

TL;DR

This paper investigates the mathematical solvability and regularity of solutions for a quasilinear magneto-quasistatic model derived from Maxwell's equations, focusing on coupled systems involving magnetic induction and electrical currents.

Contribution

It establishes well-posedness and regularity results for the coupled MQS system using gradient system theory and energy methods, advancing understanding of such models.

Findings

Proved existence and uniqueness of solutions.

Established regularity properties of solutions.

Applied gradient system framework to coupled MQS equations.

Abstract

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.