Opuscula Math. 29, no. 1 (2009), 27-39
http://dx.doi.org/10.7494/OpMath.2009.29.1.27
Opuscula Mathematica
The Cartan-Monge geometric approach to the generalized characteristics method and its application to the heat equation ut-uxx=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.
- 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
- Received: 2008-03-18.
- Revised: 2008-06-16.
- Accepted: 2008-06-22.
