Existence results for the $A-\varphi$ magnetodynamic formulation of the Maxwell system

Serge Nicaise (1)

1 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015

The $A/\varphi$ magnetodynamic Maxwell system given in its potential and space/time formulation is a popular model considered in the engineering community. We establish exitence 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.

Mots clés: Maxwell equations; potential formulation; degenerate parabolic problems.

Mots clés: degenerate parabolic problems

Domaines: Equations aux dérivées partielles [math.AP]

Serge Nicaise. Existence results for the $A-\varphi$ magnetodynamic formulation of the Maxwell system. 2013. ⟨hal-00917597⟩