Opuscula Math. 29, no. 1 (2009), 27-39
The Cartan-Monge geometric approach to the generalized characteristics method and its application to the heat equation u<sub>t</sub>-u<sub>xx</sub>=0
Jolanta Golenia
Yarema A. Prykarpatsky
Eugeniusz Wachnicki
Abstract.
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.
Keywords:
characteristics method, heat equation.
Mathematics Subject Classification:
35A30, 35K05.
About the authors ▼
Jolanta Golenia
AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Cracow, Poland
Yarema A. Prykarpatsky
Pedagogical University of Cracow, Institute of Mathematics, ul. Podchorążych 2, 30-084 Cracow, Poland; Institute of Mathematics of NAS of Ukraine, Kyiv, 01601, Ukraine; I. Franko Pedagogical University, Drohobych, Lviv region, 82100, Ukraine
Eugeniusz Wachnicki
Pedagogical University of Cracow, Institute of Mathematics, ul. Podchorążych 2, 30-084 Cracow, Poland
About the article ▼
Received: 2008-03-18.
Revised: 2008-06-16.
Accepted: 2008-06-22.
Cite this article as ▼
Jolanta Golenia, Yarema A. Prykarpatsky, Eugeniusz Wachnicki, The Cartan-Monge geometric approach to the generalized characteristics method and its application to the heat equation u<sub>t</sub>-u<sub>xx</sub>=0, Opuscula Math. 29, no. 1 (2009), 27-39,
http://dx.doi.org/10.7494/OpMath.2009.29.1.27.
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