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.
