Existence and asymptotic behavior of solutions for nonlinear Maxwell equations arising in mesoscopic electromagnetism

We consider a system of nonlinear Maxwell-type equations in the plane, which arises in the modeling of mesoscopic scale electromagnetic phenomena. After reduction to a quasi-linear equation and symmetrization, we obtain an explicit local description of the solutions in the form of power series. Subsequently, we apply general methods to show global existence of the solutions and to analyze their oscillations and asymptotic behavior.