Short Communication
Differential Equations and Mathematical Physics

Initial-boundary value problem for nonstationary heat conduction equation in a bounded domain with non-insulated lateral surface

V. D. Beybalaev^ab, T. I. Ibavov<sup>a

a</sup> Daghestan State University, Makhachkala, 367000, Russian Federation
^b Institute of Geothermal Problems and Renewable Energy Sources, Branch of the Joint Institute for High Temperatures of the Russian Academy of Sciences in Makhachkala, Makhachkala 367030, Russian Federation

Abstract: This study investigates an initial-boundary value problem for a bounded domain in thermal interaction with an external medium, incorporating memory effects through the Caputo time-fractional derivative. Heat transfer through the lateral surface is modeled as a negative heat source in the governing differential equation. An a priori estimate for the solution is established. The solution is derived by using an operational method based on the Laplace transform in time.

Keywords: memory effect, Laplace transform, nonstationary heat equationt

UDC: 517.958:536.24

MSC: 35R11, 35K05

Received: February 17, 2025
Revised: June 10, 2025
Accepted: June 17, 2025
First online: August 7, 2025

DOI: 10.14498/vsgtu2155

Bibliographic databases:

• 
•