A hierarchy of approximate modelsfor the Maxwell equations

Summary. In this paper we perform an asymptotic study of the Maxwell equations with respect to the small parameter where is the characteristic velocity associated with the physical problem and is the speed of light. This enables us to derive the quasistatic and Darwin models as respectively first and second order approximations of the Maxwell equations. Moreover, an interpretation of the obtained variational formulations gives us the appropriate boundary conditions for these models. Received May 18, 1995