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The Cartan-Monge geometric approach to the generalized characteristics method and its application to the heat equation Ut - Uxx = 0

Golenia J., Prykarpatsky Y. A., Wachnicki E.

Opuscula Mathematica

2009

Vol. 29, no. 1

27-39

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 Ut - uxx = 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.