@Article{Golenia2009,
author = "Golenia, Jolanta and Prykarpatsky, Yarema A. and Wachnicki, Eugeniusz",
title = "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",
journal = "Opuscula Math.",
year = "2009",
volume = "29",
number = "1",
pages = "27--39",
doi = "http://dx.doi.org/10.7494/OpMath.2009.29.1.27",
url = "http://dx.doi.org/10.7494/OpMath.2009.29.1.27",
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",
issn = "1232-9274"
}