Two-phase heat conduction problems with Sturm-type boundary conditions

Abstract

Abstract In this work, the solution is justified using the method of separation of variables for initial-boundary value problems of the heat conduction equation with piecewise constant thermal conductivity coefficient under Sturm-type boundary conditions (separated boundary conditions). Various cases are considered. A system of eigenfunctions of the corresponding spectral problem is constructed and it is proved that this system of eigenfunctions forms a Riesz basis. The theorem of the existence of a unique classical solution to the problem is proved.

Keywords

• Heat conduction equation
• Discontinuous coefficients
• Eigenvalues
• Eigenfunctions
• Method of separation of variables