Solution of initial-boundary value problem for heat equation with a discontinuous coefficient and general conjugation condition

Abstract

In this paper the Sturm-type boundary value problem for the heat conduction equation with a discontinuous coefficient and with a general conjugation condition is solved using the Fourier method. The considered problem may arise when solving problems describing the process of particle diffusion in turbulent plasma, as well as when modeling the process of heat propagation of the temperature field in a thin rod of finite length, consisting of two sections with different thermophysical characteristics. In addition to the boundary conditions, general conjugation conditions are specified at the contact boundary of two media with different thermophysical characteristics. The existence and uniqueness of the classical solution to the studied problem is proved.