Some questions concerning constructive methods in the theory of inverse problems

Under consideration are some questions concerning the existence of the transformations described by Yu. E. Anikonov for the second-order partial differential equations and those concerning the search of information on constructing transformations with certain conditions (for example, the divergent form of the so-obtained equation may be such a condition). Using the two-dimensional heat conductivity equation, we give examples of constructing the solutions of inverse problems. © Pleiades Publishing, Ltd. 2009.