ELECTROSTATIC BOUNDARY-VALUE-PROBLEMS OF NONLINEAR MEDIA - A PERTURBATION APPROACH

We develop perturbation expansions to solve nonlinear partial differential equations pertaining to the electrostatic boundary-value problems of nonlinear media. As an example in two dimensions, we apply the method to deal with a cylindrical inclusion in a host, both of either linear or nonlinear current-voltage characteristics, and derive the zeroth, first and second order series in the nonlinear conductivity coefficient.