<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this paper we consider first-order systems with constant coefficients 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 classification 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 appropriate basic areas, and you can try to achieve a solution of these problems by means of transform methods.</p>
</abstract>

In this paper we consider first-order systems with constant coefficients 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 classification 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 appropriate basic areas, and you can try to achieve a solution of these problems by means of transform methods.

First-order systems of linear partial differential equations: normal forms, canonical systems, transform methods

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

In this paper we consider first-order systems with constant coefficients for two real-valued functions of two real variables. This is both a problem in itself,...

First-order systems of linear partial differential equations: normal forms, canonical systems, transform methods

Published Online: Dec 11, 2014

Page range: 109 - 132

Received: Mar 31, 2014

DOI: https://doi.org/10.2478/aupcsm-2014-0009

© by Heinz Toparkus

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.