On the Product of One-Parametric Semigroups of Operators as the Solution of Certain Time-Dependent Parabolic Equations

A class of time- and space-dependent parabolic equations whose induced Lie algebras are finite dimensional is considered. It is shown that those equations can be transformed into the form of the standard heat equations in an algebraic way which can be realized by a finite number of algebraic operations if the associated Lie algebra is solvable