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

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.