{"title":"On the Temperature Distribution of a Body Heated by Radiation","authors":"Jin Woo Jang, Juan J. L. Velázquez","doi":"10.1137/23m1580917","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Mathematical Analysis, Volume 56, Issue 3, Page 3478-3508, June 2024. <br/> Abstract. In this paper, we study the temperature distribution of a body when the heat is transmitted only by radiation. The heat transmitted by convection and conduction is ignored. We consider the stationary radiative transfer equation in local thermodynamic equilibrium. We prove that the stationary radiative transfer equation coupled with the nonlocal temperature equation is well-posed in general geometries when emission-absorption or scattering of interacting radiation is considered. The emission-absorption and the scattering coefficients are assumed to be general, and they can depend on the frequency of radiation. We also establish an entropy production formula of the system which is used to prove the uniqueness of solutions for an incoming radiation with constant temperature.","PeriodicalId":51150,"journal":{"name":"SIAM Journal on Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Mathematical Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m1580917","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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Abstract
SIAM Journal on Mathematical Analysis, Volume 56, Issue 3, Page 3478-3508, June 2024. Abstract. In this paper, we study the temperature distribution of a body when the heat is transmitted only by radiation. The heat transmitted by convection and conduction is ignored. We consider the stationary radiative transfer equation in local thermodynamic equilibrium. We prove that the stationary radiative transfer equation coupled with the nonlocal temperature equation is well-posed in general geometries when emission-absorption or scattering of interacting radiation is considered. The emission-absorption and the scattering coefficients are assumed to be general, and they can depend on the frequency of radiation. We also establish an entropy production formula of the system which is used to prove the uniqueness of solutions for an incoming radiation with constant temperature.
期刊介绍：
SIAM Journal on Mathematical Analysis (SIMA) features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper has content that is primarily analytical and that employs mathematical methods in such areas as partial differential equations, the calculus of variations, functional analysis, approximation theory, harmonic or wavelet analysis, or dynamical systems. Additionally, every paper relates to a model for natural phenomena in such areas as fluid mechanics, materials science, quantum mechanics, biology, mathematical physics, or to the computational analysis of such phenomena.
Submission of a manuscript to a SIAM journal is representation by the author that the manuscript has not been published or submitted simultaneously for publication elsewhere.
Typical papers for SIMA do not exceed 35 journal pages. Substantial deviations from this page limit require that the referees, editor, and editor-in-chief be convinced that the increased length is both required by the subject matter and justified by the quality of the paper.
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