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.

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• 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
• Revised: 2008-06-16.
• Accepted: 2008-06-22.