A QUALITATIVE-ANALYSIS OF THE BEHAVIOR OF THE GALERKIN EQUATIONS RELEVANT TO NONLINEAR EDDY-CURRENT PROBLEMS

The Galerkin equations relevant to the eddy currents induced in an iro n body are considered. These equations are obtained by formulating the field problem in terms of the magnetic vector potential and by applyi ng the Galerkin method. They are shown to have a unique steady-state s olution if a certain condition on the magnetic constituitive relations hip is satisfied. In particular a T-periodic source gives rise to a un ique T-periodic solution to which all other solutions converge asympto tically independently from the initial conditions. Under the same cond ition the exponential decay of the 'transients' is shown, and an expli cit lower and upper bound for its rate is given. These structural prop erties allow us to excluse a priori that qualitatively different asymp totic behaviours, including even chaotic solutions, may occur. Numeric al simulation, when based on qualitiative information of this type, en ables us to obtain the quantitative properties in an efficient manner. In order to demonstrate the practical use of these results some numer ical experiments are presented.