The solution of the singular Volterra integral equation of the thermal problem with a uniformly moving boundary

Abstract

Boundary value problems the heat equation in domains with moving through time boundaries are becoming of great practical importance. For example, the addressing: with the theory of crystal growth, thermal oil reservoir, the problem of heat stroke by the concentrated streams of energy, the combustion layer of combustible material is reduced to the solution of problems with moving boundary. A General method of solving such kind of problems by the arbitrary law of motion of region bounds based on the theory of heat potentials simple and double layers, which leads to the solution of integral equations of type Volterra of the second kind.