First-order systems of linear partial differential equations: normal forms, canonical systems, transform methods
Abstract
In this paper we consider first-order systems with constant co efficients for two real-valued functions of two real variables. This is both a problem in itself, as well as an alternative view of the classical linear partial differential equations of second order with constant coefficients. The classi fication of the systems is done using elementary methods of linear algebra. Each type presents its special canonical form in the associated characteristic coordinate system. Then you can formulate initial value problems in appro priate basic areas, and you can try to achieve a solution of these problems by means of transform methods.
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