What question did this study set out to answer?

The research aims to solve a Sturm-type boundary value problem for the heat equation with discontinuous coefficients.

April 3, 2026Open Access

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

Key Points

The research aims to solve a Sturm-type boundary value problem for the heat equation with discontinuous coefficients.
Utilized the Fourier method to solve the boundary value problem.
Considered general conjugation conditions at the interface of two materials with different properties.
Focused on modeling heat propagation in a finite-length rod with distinct thermophysical sections.
Proved the existence of a classical solution to the heat conduction problem.
Demonstrated uniqueness of the solution under specified conditions.
Described potential applications in particle diffusion and thermal modeling.

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.

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

Key Points

Abstract

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