Singular Integral Equations for Heat Conduction Problems

Abstract

Currently, the use of contact equipment is constantly increasing. The experimental study of thermal processes is often difficult due to their transience. Therefore, in some cases, only a mathematical model can serve as the basis for obtaining additional information about dynamics of thermal processes. The monograph is devoted to formulation and study of boundary value problems for the heat conduction equation in non-cylindrical domain, the domain degenerates to a point at the initial time. The study is based on reducing the formulated problems to the second-order Volterra singular integral equation, and solving this integral equation. The methods for solving equations (when the upper and lower limits of integration coincide, the operator is not equal to zero) are not specific to ordinary Volterra equations, so they were called singular Volterra integral equations of the second kind. The monograph will be interesting to scientists, doctoral students, undergraduates, students, university teachers and everyone involved in the field of heat equations and integral equations.