Maxwell’s equations for the time-dependent electromagnetic field in a homogeneous chiral medium are reduced to a single quaternionic equation. Its fundamental solution satisfying the causality principle is obtained which allows us to solve the time-dependent chiral Maxwell system with sources.

In this paper we study a model of ferromagnetic material governed by a nonlinear Laudau-Lifschitz equation coupled with Maxwell equations. We prove the existence of weak solutions. Then we prove that all points of the !-limit set of any trajectories are solutions of the stationary model. Furthermore we derive rigourously the quasistatic model by an appropriate time average method.

The transient drift di usion model describing the charge transport in semiconductors is con sidered Poisson s equation which is usually used is replaced by Maxwell s equations The di usion and mobility coe cients and the dielectric and magnetic susceptibilities may depend on the space variables Global existence and convergence to the thermal equilibrium is shown

/ d e i \ (is) y — r*?W' = -/"Y'. \dx* c h / The factor — r on the right-hand side of this equation shows that the Dirac equation for an electron is not invariant under inversions. However, if we set 0? = O and JU = 0, then equation (15) is numerically invariant under inversions. This is done in the neutrino theory of light. Hence that theory has the same invariance properties as the Maxwell th...