On the integral equation of the boundary value problem for the essentially loaded differential heat operator

Abstract

In the article the Volterra integral equations of the second kind with the given kernel are investigated. This kind of integral equations arises in the solving of some boundary value problems for essential loaded differential heat operator in an unbounded domain. The theory of boundary value problems for essential loaded differential parabolic equations is very important not only for the modeling of the physical, technical and application processes, but also in the experimental studies. The test problems are also connected with mathematical modeling of thermal processes in the electric arc of the high-current breaking devices. Experimental studies of these phenomena are difficult because of their transience and in some cases only a mathematical model is capable to provide adequate information about their dynamics, so the test material is highly relevant in modern science.