Opuscula Mathematica
Opuscula Math. 29, no. 1 (), 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




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.
Cite this article as:
Jolanta Golenia, Yarema A. Prykarpatsky, Eugeniusz Wachnicki, The Cartan-Monge geometric approach to the generalized characteristics method and its application to the heat equation ut-uxx=0, Opuscula Math. 29, no. 1 (2009), 27-39, http://dx.doi.org/10.7494/OpMath.2009.29.1.27
 
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ISSN 1232−9274, e-ISSN 2300−6919, DOI http://dx.doi.org/10.7494/OpMath
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