Boundary value problems for essentially-loaded parabolic equation

Abstract

In this paper we investigate the first boundary value problem for essentially loaded equation of heat conduction, i.e. when laden terms are derivatives for any finite order. It is shown that if the point of load is fixed, this problem is uniquely solvable. The stated boundary problem is reduced to the Volterra integral equation of the second kind. Estimates of the kernel of the integral equation are made, which indicate a weak singularity of the kernel. It is shown that if the point of load is fixed, then the stated boundary problem is uniquely solvable.