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Well-posedness of the microwave heating problem
- Authors: Tsangia B.1
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Affiliations:
- Mongolian University of Science and Technology
- Issue: Vol 32, No 2 (2024)
- Pages: 222-233
- Section: Articles
- URL: https://journals.rudn.ru/miph/article/view/41390
- DOI: https://doi.org/10.22363/2658-4670-2024-32-2-222-233
- EDN: https://elibrary.ru/CDJVIL
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Abstract
A number of initial boundary-value problems of classical mathematical physics is generally represented in the linear operator equation and its well-posedness and causality in a Hilbert space setting was established. If a problem has a unique solution and the solution continuously depends on given data, then the problem is called well-posed. The independence of the future behavior of a solution until a certain time indicates the causality of the solution. In this article, we established the well-posedness and causality of the solution of the evolutionary problems with a perturbation, which is defined by a quadratic form. As an example, we considered the coupled system of the heat and Maxwell’s equations (the microwave heating problem).
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1. Introduction Here we consider a non-linear, coupled system in thermoelectricity. Thermoelectric effects are viewed as the result of the mutual interference of heat flow and electric flow in a system. The interaction of thermal and electric processes is modeled by the heat equationAbout the authors
Baljinnyam Tsangia
Mongolian University of Science and Technology
Author for correspondence.
Email: Baljinnyam.Tsangia@must.edu.mn
ORCID iD: 0000-0002-3331-2516
Dr.rer.nat, Lecturer of Department of Mathematics, School of Applied Sciences, Mongolian University of Science and Technology
Ulaanbaatar, MongoliaReferences
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