WELL-POSEDNESS OF AN INITIAL BOUNDARY VALUE PROBLEM FROM LASER DYNAMICS

Abstract

In this paper a mathematical model, consisting of nonlinear first-order ordinary and partial differential equations with initial and boundary conditions, for the dynamical behavior of multisection DFB (distributed feedback) semiconductor lasers is investigated. We introduce a suitable weak formulation and prove existence, uniqueness and regularity properties of the solutions. The assumptions on the data are quite general, in particular, the physically relevant case of piecewise smooth, but discontinuous with respect to space and time coefficients in the equations and in the boundary conditions is included.