Title :

Existence results for the $\mathbf{A}-\varphi-\mathbf{B}$ magnetodynamic formulation of the Maxwell system with skin and proximity effects

Author(s) :

Creusé, Emmanuel [Auteur]
Laboratoire de Matériaux Céramiques et de Mathématiques [CERAMATHS]
Reliable numerical approximations of dissipative systems [RAPSODI]
Nicaise, Serge [Auteur correspondant]
Laboratoire de Matériaux Céramiques et de Mathématiques [CERAMATHS]
Sabariego, Ruth [Auteur]
Department of Electrical Engineering - K.U.Leuven [ESAT/SCD-COSIC]

Journal title :

Applicable Analysis

Pages :

3103-3121

Publisher :

Taylor & Francis

Publication date :

2022

ISSN :

0003-6811

English keyword(s) :

Maxwell equations
potential formulation
degenerate parabolic problems
Eddy current losses

HAL domain(s) :

Sciences de l'ingénieur [physics]/Electromagnétisme
Mathématiques [math]/Equations aux dérivées partielles [math.AP]

English abstract : [en]

The $\mathbf{A}-\varphi-\mathbf{B}$ magnetodynamic Maxwell system given in its potential and space-time formulation is a popular model considered in the engineering community. It allows to model some phenomena such as eddy ...
Show more >The $\mathbf{A}-\varphi-\mathbf{B}$ magnetodynamic Maxwell system given in its potential and space-time formulation is a popular model considered in the engineering community. It allows to model some phenomena such as eddy current losses in multiple turn winding. Indeed, in some cases, they can significantly alter the performance of the devices, and consequently can no more be neglegted. It turns out that this model is not yet analytically studied, therefore we here consider its well-posedness. First, the existence of strong solutions with the help of the theory of Showalter on degenerated parabolic problems is established. Second, using energy estimates, existence and uniqueness of the weak solution of the $\mathbf{A}-\varphi-\mathbf{B}$ system is deduced.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL