A singular limit in a nonlinear problem arising in electromagnetism
Initial boundary value problems associated with Maxwell's equations for linear media with non-linear conducting inclusions are considered. The limit of vanishing dielectricity \(\epsilon\) in the conducting region leading to the eddy current approximation with a non-linear Ohm's law is of particular interest. Based on existence and uniqueness for the positive dielectricity case, existence of the eddy current limit case is shown by controlling the singular limit \(\epsilon\to0^+\) in the non-linearly conducting region. The limit problem is of hyperbolic-parabolic mixed type. In the two final sections of the paper weak and strong asymptotics of the solution to the limit problem for large times are considered.
scientific article; zbMATH DE number 5989616