TY  - JOUR
ID  - Golenia2009
LB  - Golenia2009
AU  - Golenia, Jolanta
AU  - Prykarpatsky, Yarema A.
AU  - Wachnicki, Eugeniusz
TI  - 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
ST  - 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
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2009
VL  - 29
IS  - 1
SP  - 27
EP  - 39
DO  - http://dx.doi.org/10.7494/OpMath.2009.29.1.27
UR  - http://dx.doi.org/10.7494/OpMath.2009.29.1.27
AB  - 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.
KW  - characteristics method
KW  - heat equation
SN  - 1232-9274
ER  -