The Cartan-Monge geometric approach to the generalized characteristics method and its application to the heat equation u_{t}-u_{xx}=0

The Cartan-Monge geometric approach to the generalized characteristics method and its application to the heat equation u_{t}-u_{xx}=0

The generalized Cartan-Monge type approach to the characteristics method is discussed from the geometric point of view. Its application to the classical one-dimensional linear heat equation \(u_t-u_{xx}=0\) is presented. It is shown that the corresponding exact solution of the Cauchy problem can be...

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Veröffentlicht in:Rocznik Akademii Górniczo-Hutniczej im. Stanisława Staszica. Opuscula Mathematica 2009-01, Vol.29 (1), p.27-39
Hauptverfasser: Jolanta Golenia, Yarema A. Prykarpatsky, Eugeniusz Wachnicki
Format: Artikel
Sprache:eng
Schlagworte:
characteristics method
heat equation
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Zusammenfassung:The generalized Cartan-Monge type approach to the characteristics method is discussed from the geometric point of view. Its application to the classical one-dimensional linear heat equation \(u_t-u_{xx}=0\) is presented. It is shown that the corresponding exact solution of the Cauchy problem can be represented in a classical functional-analytic Gauss type form.
ISSN:1232-9274
DOI:10.7494/OpMath.2009.29.1.27