Resolvability of boundary problems describing film atom diffusion in underlying surface at formation of thin-film structures

Relevance of the work. Extraction of geo assets requires the development of new technological solutions for their production, for example, the coating of drill screws with anticorrosion agents. A solution to this problem is possible using diffusion lacquer coating (corrosion inhibitor) on underlying...

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Autors principals:	Tarasenko, E. O., Тарасенко, Е. О., Gladkov, A. V., Гладков, А. В.
Format:	Статья
Idioma:	English
Publicat:	Tomsk Polytechnic University, Publishing House 2018
Matèries:	Boundary problem Diffusive growth Resolvability Substrate Thin film Underlying surface
Accés en línia:	https://www.scopus.com/record/display.uri?eid=2-s2.0-85019420191&origin=resultslist&sort=plf-f&src=s&nlo=1&nlr=20&nls=afprfnm-t&affilName=north+caucasus+federal+university&sid=d363385a496a31df70e3a34d3fef9a28&sot=afnl&sdt=sisr&cluster=scopubyr%2c%222016%22%2ct&sl=53&s=%28AF-ID%28%22North+Caucasus+Federal+University%22+60070541%29%29&ref=%28Resolvability+of+boundary+problems+describing+film+atom+diffusion+in+underlying+surface+at+formation+of+thin-film+structures%29&relpos=0&citeCnt=0&searchTerm= https://dspace.ncfu.ru/handle/20.500.12258/3353
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spelling	ir-20.500.12258-33532020-07-30T12:30:30Z Resolvability of boundary problems describing film atom diffusion in underlying surface at formation of thin-film structures Tarasenko, E. O. Тарасенко, Е. О. Gladkov, A. V. Гладков, А. В. Boundary problem Diffusive growth Resolvability Substrate Thin film Underlying surface Relevance of the work. Extraction of geo assets requires the development of new technological solutions for their production, for example, the coating of drill screws with anticorrosion agents. A solution to this problem is possible using diffusion lacquer coating (corrosion inhibitor) on underlying surface (auger). The mathematization of such physical process as diffusion growth of thin films on the underlying surface is currently unexplored. In mathematical models the question on the existence and uniqueness of the solution of boundary-value problems describing the specified physical process often arises. Many domestic and foreign scientists have studied the analytical and numerical methods for solving the initial-boundary value problems, in which it is originally explicitly or implicitly assumed that the solution of the problem exists and it is unique. As a rule, the authors of publications devoted to various problems of mathematical modeling of diffusion, either do not address this question at all (about the existence and uniqueness of the solution) or refer to the classic works without good reason. Therefore, the studies on solvability of boundary value problems carried out in the paper are relevant. The aim of the research is to develop the criteria of resolvability (existence and uniqueness) of the boundary problems arising at mathematical modeling of the thin-film structure growth on underlying surface in various spaces. Research methods. The achievement of a goal is based on correct use of results and methods of the equations of mathematical physics, the integrated equations, the mathematical analysis, the equations in private derivatives, physics of a solid body, a crystallography. Results. The authors have studied the resolvability of the boundary problems describing the diffusive growth of thin films on substrates; developed the criteria of existence and uniqueness of the solution of the specified tasks in various spaces. Conclusions. At mathematical modeling of diffusive growth of a thin film on underlying surface the authors developed the theorems (criteria) providing resolvability (existence and uniqueness of the decision) of initial-boundary tasks. The paper considers the boundary problems for cases of full reflection and absorption of atoms of a film by the underlying surface. The present article is of considerable interest in applied research, and allows answering a question whether it is possible to proceed immediately to a numerical (or possibly analytic) solution of the specific boundary value problem describing the diffusion growth of thin-film structures on substrates, or carry out further researches on its regularization 2018-10-30T10:19:11Z 2018-10-30T10:19:11Z 2016 Статья Tarasenko, E.O., Gladkov, A.V., Malikova, N.V. Resolvability of boundary problems describing film atom diffusion in underlying surface at formation of thin-film structures // Bulletin of the Tomsk Polytechnic University, Geo Assets Engineering. - 2016. - Volume 327. - Issue 2. - Pages 125-132 https://www.scopus.com/record/display.uri?eid=2-s2.0-85019420191&origin=resultslist&sort=plf-f&src=s&nlo=1&nlr=20&nls=afprfnm-t&affilName=north+caucasus+federal+university&sid=d363385a496a31df70e3a34d3fef9a28&sot=afnl&sdt=sisr&cluster=scopubyr%2c%222016%22%2ct&sl=53&s=%28AF-ID%28%22North+Caucasus+Federal+University%22+60070541%29%29&ref=%28Resolvability+of+boundary+problems+describing+film+atom+diffusion+in+underlying+surface+at+formation+of+thin-film+structures%29&relpos=0&citeCnt=0&searchTerm= http://hdl.handle.net/20.500.12258/3353 en Bulletin of the Tomsk Polytechnic University, Geo Assets Engineering application/pdf Tomsk Polytechnic University, Publishing House
institution	СКФУ
collection	Репозиторий
language	English
topic	Boundary problem Diffusive growth Resolvability Substrate Thin film Underlying surface
spellingShingle	Boundary problem Diffusive growth Resolvability Substrate Thin film Underlying surface Tarasenko, E. O. Тарасенко, Е. О. Gladkov, A. V. Гладков, А. В. Resolvability of boundary problems describing film atom diffusion in underlying surface at formation of thin-film structures
description	Relevance of the work. Extraction of geo assets requires the development of new technological solutions for their production, for example, the coating of drill screws with anticorrosion agents. A solution to this problem is possible using diffusion lacquer coating (corrosion inhibitor) on underlying surface (auger). The mathematization of such physical process as diffusion growth of thin films on the underlying surface is currently unexplored. In mathematical models the question on the existence and uniqueness of the solution of boundary-value problems describing the specified physical process often arises. Many domestic and foreign scientists have studied the analytical and numerical methods for solving the initial-boundary value problems, in which it is originally explicitly or implicitly assumed that the solution of the problem exists and it is unique. As a rule, the authors of publications devoted to various problems of mathematical modeling of diffusion, either do not address this question at all (about the existence and uniqueness of the solution) or refer to the classic works without good reason. Therefore, the studies on solvability of boundary value problems carried out in the paper are relevant. The aim of the research is to develop the criteria of resolvability (existence and uniqueness) of the boundary problems arising at mathematical modeling of the thin-film structure growth on underlying surface in various spaces. Research methods. The achievement of a goal is based on correct use of results and methods of the equations of mathematical physics, the integrated equations, the mathematical analysis, the equations in private derivatives, physics of a solid body, a crystallography. Results. The authors have studied the resolvability of the boundary problems describing the diffusive growth of thin films on substrates; developed the criteria of existence and uniqueness of the solution of the specified tasks in various spaces. Conclusions. At mathematical modeling of diffusive growth of a thin film on underlying surface the authors developed the theorems (criteria) providing resolvability (existence and uniqueness of the decision) of initial-boundary tasks. The paper considers the boundary problems for cases of full reflection and absorption of atoms of a film by the underlying surface. The present article is of considerable interest in applied research, and allows answering a question whether it is possible to proceed immediately to a numerical (or possibly analytic) solution of the specific boundary value problem describing the diffusion growth of thin-film structures on substrates, or carry out further researches on its regularization
format	Статья
author	Tarasenko, E. O. Тарасенко, Е. О. Gladkov, A. V. Гладков, А. В.
author_facet	Tarasenko, E. O. Тарасенко, Е. О. Gladkov, A. V. Гладков, А. В.
author_sort	Tarasenko, E. O.
title	Resolvability of boundary problems describing film atom diffusion in underlying surface at formation of thin-film structures
title_short	Resolvability of boundary problems describing film atom diffusion in underlying surface at formation of thin-film structures
title_full	Resolvability of boundary problems describing film atom diffusion in underlying surface at formation of thin-film structures
title_fullStr	Resolvability of boundary problems describing film atom diffusion in underlying surface at formation of thin-film structures
title_full_unstemmed	Resolvability of boundary problems describing film atom diffusion in underlying surface at formation of thin-film structures
title_sort	resolvability of boundary problems describing film atom diffusion in underlying surface at formation of thin-film structures
publisher	Tomsk Polytechnic University, Publishing House
publishDate	2018
url	https://www.scopus.com/record/display.uri?eid=2-s2.0-85019420191&origin=resultslist&sort=plf-f&src=s&nlo=1&nlr=20&nls=afprfnm-t&affilName=north+caucasus+federal+university&sid=d363385a496a31df70e3a34d3fef9a28&sot=afnl&sdt=sisr&cluster=scopubyr%2c%222016%22%2ct&sl=53&s=%28AF-ID%28%22North+Caucasus+Federal+University%22+60070541%29%29&ref=%28Resolvability+of+boundary+problems+describing+film+atom+diffusion+in+underlying+surface+at+formation+of+thin-film+structures%29&relpos=0&citeCnt=0&searchTerm= https://dspace.ncfu.ru/handle/20.500.12258/3353
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Resolvability of boundary problems describing film atom diffusion in underlying surface at formation of thin-film structures

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