Existence results for the $\mathbf{A}-\v ...
Document type :
Compte-rendu et recension critique d'ouvrage
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]
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
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]
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 >
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
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