  The coupled Maxwell-Lorentz system describes feed-back action of
electromagnetic fields in classical electrodynamics. When applied to
point-charge sources (viewed as limiting cases of charged fluids) the resulting
nonlinear weakly hyperbolic system lies beyond the scope of classical
distribution theory. Using regularized derivatives in the framework of
Colombeau algebras of generalized functions we analyze a two-dimensional
analogue of the Maxwell-Lorentz system. After establishing existence and
uniqueness of solutions in this setting we derive some results on
distributional limits of solutions with $\delta$-like initial values.
