Investigation of the model for the essentially loaded heat equation

Abstract

The studied problem for the essentially loaded heat equation is connected with mathematical modeling of thermophysical processes in the electric arc of high-current disconnecting devices. Experimental studies of such phenomena are difficult due to their transience, and in some cases only a mathematical model is able to provide adequate information about their dynamics. The study of the mathematical model is carried out when the order of the derivative in the loaded summand is less than, equal to and greater than the order of the differential part of the heat equation, at a fixed point of the load and in the case when the load point moves at a variable speed. The article is focused mainly on scientific researchers engaged in practical applications of loaded differential equations.