Existence results for the A & φ magnetodynamic formulation of the Maxwell system

Abstract

The magnetodynamic Maxwell system given in its potential and space/time formulation is a popular model considered in the engineering community. We establish existence of strong solutions with the help of the theory of Showalter on degenerated parabolic problems; using energy estimates, existence of weak solutions are also deduced.

Keywords:

• Maxwell equations
• potential formulation
• degenerate parabolic problems

AMS Subject Classifications:

• 35H65
• 35Q60
• 78A25

Acknowledgments

I thank Emmanuel Creusé (LPP UMR 8524 and INRIA Lille Nord Europe, Université de Lille 1) and Roberta Tittarelli (LPP UMR 8524 and L2EP, Université de Lille 1) for their introduction to this problem and very fruitful discussions about this work.