Construction of the Solution to a Second-Order Partial DifferentialEquation of Parabolic Type with Multiple Variables by the Methodof Additional Argument

Abstract

The article examines a parabolic-type partial differential equation. It is well known that the phenomenon of heat transfer in physics is modeled by parabolic-type equations. Therefore, the problems of constructing solutions to such equations are of both theoretical and practical interest. In our work there is considered the case of multiple variables and equation of second order. The purpose of the work is to apply the method of additional argument to parabolic-type equations. The Cauchy-Dirichlet problem is investigated, and its unique solution is established. The obtained result is illustrated by
a concrete example. Similar results can be extended to other types of partial differential equations.