On a Singular Limit Problem for Nonlinear Maxwell's Equations
Hong‐Ming Yin · Journal of Differential Equations · 1999
In this paper we study the following nonlinear Maxwell's equations, εEt+σ(x, |E|) E=∇×H+F, Ht+∇×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.