An eddy current problem with a nonlinear evolution boundary condition

Our paper is devoted to a study of an eddy current problem with a nonlinear evolution degenerate boundary condition of the type ν × E = ν × ∂ t a ( H × ν ) with a power-law nonlinearity. We have designed a nonlinear numerical scheme for approximation in suitable function spaces. The well-posedness of the problem is addressed and the error estimates are derived. Monotonicity methods and the Minty–Browder argument are used in the proofs.