Zeitschrift für Analysis und ihre Anwendungen Vol. 19, No. 1, pp. 147158 (2000) 

Regularized Derivatives in a 2Dimensional Model of SelfInteracting Fields with Singular DataG. Hörmann and M. KunzingerUniv. Wien, Inst. Math., A1090 Wien, Austria, email: guenther.hoermann@univie.ac.at & michael.kunzinger@univie.ac.atAbstract: The coupled MaxwellLorentz system describes feedback action of electromagnetic fields in classical electrodynamics. When applied to pointcharge 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 twodimensional analogue of the MaxwellLorentz 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. Keywords: regularized derivatives, Colombeau algebras, selfinteraction, weak hyperbolicity, MaxwellLorentz system Classification (MSC2000): 35Dxx, 46F10, 35Lxx, 78A25 Full text of the article:
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