Some remarks on a class of plane, linear boundary value problems

A class of mathematical problems which arise in magnetohydrodynamics is discussed. Various special problems in the study of heat convection, rotating fluids and solid mechanics fall within the category considered. A pair of linear, coupled partial differential equations which involve a parameter M are studied. The region of interest is a rectangle and various sets of linear boundary conditions are considered. In this paper a new approach is developed for the asymptotic analysis in the limit as M goes to infinity. Detailed comment is made on the successes and failures of the new approach and on its relationship to previous work.