ON A SINGULAR LIMIT PROBLEM FOR NONLINEAR MAXWELL’S EQUATIONS

HONG-MING YIN

Abstract. In this paper we study the following nonlinear Maxwell’s equations εE_{t} + σ(x, |E|)E = ∇ × H + F, H_{t} + ∇ × E = 0, where σ(x, s) is a monotone graph of s. It is shown that the system has a unique weak solution. Moreover, the limit of the solution as ε → 0 converges to the solution of quasi-stationary Maxwell’s equations.