A transient eddy current problem on a moving domain. Mathematical analysis

The aim of this paper is to introduce and analyze a weak formulation of the transient eddy current problem governing electromagnetic forming in the axisymmetric case. The resulting problem is degenerate parabolic with the time derivative acting on a moving subdomain. Because of this, we have to resort to regularization arguments in order to prove its well-posedness. We also investigate additional regularity of the solution- Xunta de Galicia under research projects INCITE09 207 047 PR and INCITE09 291 083 PR, - Ministerio de Ciencia e Innovación (Spain) under research projects Consolider MATHEMATICA CSD2006-00032, MTM2008-02483 and MTM2009-07749. - MECESUP fellowship (Chile). - BASAL project, CMM, Universidad de Chile (Chile), Anillo ANANUM, ACT1118, CONICYT (Chile).S