THERMAL SCIENCE

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Van Thi Kim Ho

NON-CLASSICAL HEAT EQUATION WITH SINGULAR MEMORY TERM

ABSTRACT
In this paper, we consider the non-classical heat equation with singular memory term. This equation has many applications in various fields, for example liquids mechanics, solid mechanics, and heat conduction theory first, we prove that the solution exists locally in time. Then we investigate the converegence of the mild solution of non-classical heat equation, and the mild solution of classical heat equation.
KEYWORDS
non-classical heat equation, memory term, local existence, banach fixed point theorem
PAPER SUBMITTED: 2021-03-02
PAPER REVISED: 2021-03-25
PAPER ACCEPTED: 2021-04-02
PUBLISHED ONLINE: 2021-12-18
DOI REFERENCE: https://doi.org/10.2298/TSCI21S2219H
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2021, VOLUME 25, ISSUE Special issue 2, PAGES [219 - 226]
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Non-classical heat equation with singular memory term

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence