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

Opuscula Mathematica

Jolanta Golenia¹  Yarema A. Prykarpatsky²  Eugeniusz Wachnicki² 

[1] AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Cracow, Poland;Pedagogical University of Cracow, Institute of Mathematics, ul. Podchorążych 2, 30-084 Cracow, Poland;

关键词: characteristics method;    heat equation;   

DOI  :  http://dx.doi.org/10.7494/OpMath.2009.29.1.27

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown