Extreme properties of solutions of a parabolic equation


Rational procedures and properties of solutions of limiting problems have been considered for equations and limiting problems with partial derivatives of a parabolic type. It was proved that such limiting problems for parabolic equations admitting the group of self-transformations were necessary conditions for a minimum of positive functionals; furthermore, the Crocco equation was proved to be equivalent to a canonical system and its applicable functional was shown to be found at once. It was also demonstrated that someone was able to bring a parabolic equation in its original notation into a canonical form using additive doubling variables.