Nonstationary Radiative–Conductive Heat Transfer Problem in a Semitransparent Body with Absolutely Black Inclusions

Nonstationary Radiative–Conductive Heat Transfer Problem in a Semitransparent Body with Absolutely Black Inclusions

The paper is devoted to a nonstationary initial–boundary value problem governing complex heat exchange in a convex semitransparent body containing several absolutely black inclusions. The existence and uniqueness of a weak solution to this problem are proven herein. In addition, the stability of sol...

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Main Author: Andrey Amosov
Format: Article
Language:English
Published: MDPI AG 2021-06-01
Series:Mathematics
Subjects:
radiative–conductive heat transfer problem
radiative transfer equation
nonlinear initial–boundary value problem
stability of solutions with respect to data
comparison theorem
Online Access:https://www.mdpi.com/2227-7390/9/13/1471
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spelling doaj-504f6dd205944ab288b3ea4a002327822021-07-15T15:41:23ZengMDPI AGMathematics2227-73902021-06-0191471147110.3390/math9131471Nonstationary Radiative–Conductive Heat Transfer Problem in a Semitransparent Body with Absolutely Black InclusionsAndrey Amosov0Department of Mathematical and Computer Modelling, National Research University “Moscow Power Engineering Institute”, 111250 Krasnokazarmennay St. 14, 111250 Moscow, RussiaThe paper is devoted to a nonstationary initial–boundary value problem governing complex heat exchange in a convex semitransparent body containing several absolutely black inclusions. The existence and uniqueness of a weak solution to this problem are proven herein. In addition, the stability of solutions with respect to data, a comparison theorem and the results of improving the properties of solutions with an increase in the summability of the data were established. All results are global in terms of time and data.https://www.mdpi.com/2227-7390/9/13/1471radiative–conductive heat transfer problemradiative transfer equationnonlinear initial–boundary value problemstability of solutions with respect to datacomparison theorem
collection DOAJ
language English
format Article
sources DOAJ
author Andrey Amosov
spellingShingle Andrey Amosov
Nonstationary Radiative–Conductive Heat Transfer Problem in a Semitransparent Body with Absolutely Black Inclusions
Mathematics
radiative–conductive heat transfer problem
radiative transfer equation
nonlinear initial–boundary value problem
stability of solutions with respect to data
comparison theorem
author_facet Andrey Amosov
author_sort Andrey Amosov
title Nonstationary Radiative–Conductive Heat Transfer Problem in a Semitransparent Body with Absolutely Black Inclusions
title_short Nonstationary Radiative–Conductive Heat Transfer Problem in a Semitransparent Body with Absolutely Black Inclusions
title_full Nonstationary Radiative–Conductive Heat Transfer Problem in a Semitransparent Body with Absolutely Black Inclusions
title_fullStr Nonstationary Radiative–Conductive Heat Transfer Problem in a Semitransparent Body with Absolutely Black Inclusions
title_full_unstemmed Nonstationary Radiative–Conductive Heat Transfer Problem in a Semitransparent Body with Absolutely Black Inclusions
title_sort nonstationary radiative–conductive heat transfer problem in a semitransparent body with absolutely black inclusions
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2021-06-01
description The paper is devoted to a nonstationary initial–boundary value problem governing complex heat exchange in a convex semitransparent body containing several absolutely black inclusions. The existence and uniqueness of a weak solution to this problem are proven herein. In addition, the stability of solutions with respect to data, a comparison theorem and the results of improving the properties of solutions with an increase in the summability of the data were established. All results are global in terms of time and data.
topic radiative–conductive heat transfer problem
radiative transfer equation
nonlinear initial–boundary value problem
stability of solutions with respect to data
comparison theorem
url https://www.mdpi.com/2227-7390/9/13/1471
work_keys_str_mv AT andreyamosov nonstationaryradiativeconductiveheattransferprobleminasemitransparentbodywithabsolutelyblackinclusions
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