Some Remarks on a Class of Plane, Linear Boundary Value Problems

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Abstract
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 M ↑ ω. Detailed comment is made on the successes and failures of the new approach and on its relationship to previous work.

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