Group properties of nonlinear heat equations and solution of inverse problems
Abstract
The inverse problem in heat conduction theory of identifying the heat conducting medium is studied. The necessary and sufficient conditions for the uniqueness of the solution to the problem are established in terms of the group properties of a nonlinear heat equation. An effective procedure for solving the identification problem is proposed which makes use of certain invariantgroup solutions of the heat equation.
 Publication:

Akademiia Nauk BSSR Doklady
 Pub Date:
 November 1975
 Bibcode:
 1975DoBel..19..992F
 Keywords:

 Conductive Heat Transfer;
 Group Theory;
 Thermal Conductivity;
 Thermodynamics;
 Invariance;
 Lie Groups;
 Nonlinear Equations;
 Temperature Distribution;
 Fluid Mechanics and Heat Transfer