A model of wave propagation in a nonlinear superconducting dielectric (Q1198730)

Authors's summary: The problem of a linearly polarized plane electromagnetic wave propagating in an unbounded domain occupied by a nonlinear dielectric is considered under the assumption that the conduction current is inversely proportional to the magnetic permeability and directly proportional to the electric field strength. We prove that, in the limit of vanishing magnetic permeability, the electromagnetic wave tends to one which propagates with infinite speed: the demonstration hinges upon proving that the globally existing solutions of a nonlinearly damped, nonlinear wave equation converge weakly in \(L^ 2\) to the unique classical solution of an associated heat equations.