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

Heinz Toparkus

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica (2014)

  • Volume: 13, page 109-132
  • ISSN: 2300-133X

Abstract

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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.

How to cite

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Heinz Toparkus. "First-order systems of linear partial differential equations: normal forms, canonical systems, transform methods." Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica 13 (2014): 109-132. <http://eudml.org/doc/268779>.

@article{HeinzToparkus2014,
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.},
author = {Heinz Toparkus},
journal = {Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica},
keywords = {characteristic coordinate system},
language = {eng},
pages = {109-132},
title = {First-order systems of linear partial differential equations: normal forms, canonical systems, transform methods},
url = {http://eudml.org/doc/268779},
volume = {13},
year = {2014},
}

TY - JOUR
AU - Heinz Toparkus
TI - First-order systems of linear partial differential equations: normal forms, canonical systems, transform methods
JO - Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
PY - 2014
VL - 13
SP - 109
EP - 132
AB - 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.
LA - eng
KW - characteristic coordinate system
UR - http://eudml.org/doc/268779
ER -

References

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