Generalized Statements and Properties of Models of Transport Processes in Domains with Cuts

We study a linear parabolic system in a domain with a thin low-permeable inclusion. A new formulation of the problem is obtained with unknowns (u, ω). Under this approach, the main second-order parabolic equation is converted to a set of first-order partial differential equations with distributional...

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Vydané v:	Cybernetics and systems analysis Ročník 52; číslo 6; s. 931 - 942
Hlavní autori:	Nomirovskii, D. A., Vostrikov, O. I.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York Springer US 01.11.2016 Springer Springer Nature B.V
Predmet:	Analysis Artificial Intelligence Control Cybernetics Differential equations Heat transfer Inclusions Materials science Mathematical analysis Mathematical models Mathematics Mathematics and Statistics Partial differential equations Processor Architectures Software Engineering/Programming and Operating Systems Studies Systems analysis Systems Theory Transport processes Transportation models transport conditions discontinuous solution generalized functions parabolic equation
ISSN:	1060-0396, 1573-8337
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Abstract	We study a linear parabolic system in a domain with a thin low-permeable inclusion. A new formulation of the problem is obtained with unknowns (u, ω). Under this approach, the main second-order parabolic equation is converted to a set of first-order partial differential equations with distributional coefficients. The relations of the approach to the classical and weak formulations of the problem are analyzed.
AbstractList	We study a linear parabolic system in a domain with a thin low-permeable inclusion. A new formulation of the problem is obtained with unknowns (u, [omega]). Under this approach, the main second-order parabolic equation is converted to a set of first-order partial differential equations with distributional coefficients. The relations of the approach to the classical and weak formulations of the problem are analyzed. Keywords: parabolic equation, discontinuous solution, transport conditions, generalized functions. We study a linear parabolic system in a domain with a thin low-permeable inclusion. A new formulation of the problem is obtained with unknowns (u, omega ). Under this approach, the main second-order parabolic equation is converted to a set of first-order partial differential equations with distributional coefficients. The relations of the approach to the classical and weak formulations of the problem are analyzed. We study a linear parabolic system in a domain with a thin low-permeable inclusion. A new formulation of the problem is obtained with unknowns (u, ω). Under this approach, the main second-order parabolic equation is converted to a set of first-order partial differential equations with distributional coefficients. The relations of the approach to the classical and weak formulations of the problem are analyzed.
Audience	Academic
Author	Nomirovskii, D. A. Vostrikov, O. I.
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Cites_doi	10.1007/s10625-005-0227-x 10.1007/978-1-4614-0619-8 10.1090/S0025-5718-1981-0606505-9 10.1134/S096554250606008X 10.1016/j.jde.2006.09.025 10.1017/S095679251100012X
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References	SemenovVVSolvability of a parabolic transmission problem with the condition of a generalized proper lumped sourceDifferential Equations2005416878886220579210.1007/s10625-005-0227-x1086.35020 NomirovskiiDAApproximate method for solving the boundary-value problem for a parabolic equation with inhomogeneous transmission conditions of nonideal contact typeComputational Mathematics and Mathematics Physics20064669951006228536410.1134/S096554250606008X LyashkoIIDemchenkoVFGeneralized statements of problems of heat and mass transfer in layered media1987KyivPrepr. AN UkrSSR, V. M. Glushkov Inst. of Cybernetics KlyushinDALyashkoSINomirovskiiDAPetuninYISemenovVVGeneralized Solutions of Operator Equations and Extreme Elements2012New YorkSpringer10.1007/978-1-4614-0619-81240.47002 SergienkoIVDeinekaVSSystems Analysis of Multicomponent Distributed Systems [in Russian]2009KyivNaukova Dumka1297.93076 NomirovskiiDGeneralized solvability and optimization of a parabolic system with a discontinuous solutionJ. of Differential Equations20072331121229026910.1016/j.jde.2006.09.0251113.35025 MercierBOsbornJRappazJRaviartPAEigenvalue approximation by mixed and hybrid methodsMathematics of Computation19813615442745360650510.1090/S0025-5718-1981-0606505-90472.65080 DeinekaVSSergienkoIVSkopetskyVVModels and Methods to Solve Problems with Interface Conditions [in Russian]1998KyivNaukova Dumka DemchenkoVFKrivtsunIVPavlykVODiltheyULisnyiOBNakvasyukVVProblems of heat, mass and charge transfer with discontinuous solutionsEuropean J. of Applied Math.2011224365380281291710.1017/S095679251100012X1227.35129 NomirovskiiDAGeneralized resolvability of parabolic systems with nonhomogeneous transmission conditions of nonideal contact typeDiff. Uravn.200440101467147722000131182.35138 Fumio Kikuchi, “Numerical analysis of a mixed finite element method for plate buckling problems,” Inst. of Space and Aeronautical Science, Univ. of Tokyo Report, No. 584, September, 165–190 (1980). LyashkoSINomirovskiiDAPetuninYISemenovVVHilbert’s 20th Problem. Generalized Solutions of Functional Equations [in Russian]2009MoscowI.D. Vil’yams DA Nomirovskii (9895_CR7) 2004; 40 VF Demchenko (9895_CR6) 2011; 22 VV Semenov (9895_CR3) 2005; 41 IV Sergienko (9895_CR1) 2009 VS Deineka (9895_CR2) 1998 SI Lyashko (9895_CR9) 2009 DA Klyushin (9895_CR10) 2012 B Mercier (9895_CR12) 1981; 36 II Lyashko (9895_CR5) 1987 D Nomirovskii (9895_CR8) 2007; 233 DA Nomirovskii (9895_CR4) 2006; 46 9895_CR11
References_xml	– reference: NomirovskiiDAGeneralized resolvability of parabolic systems with nonhomogeneous transmission conditions of nonideal contact typeDiff. Uravn.200440101467147722000131182.35138 – reference: NomirovskiiDGeneralized solvability and optimization of a parabolic system with a discontinuous solutionJ. of Differential Equations20072331121229026910.1016/j.jde.2006.09.0251113.35025 – reference: LyashkoSINomirovskiiDAPetuninYISemenovVVHilbert’s 20th Problem. Generalized Solutions of Functional Equations [in Russian]2009MoscowI.D. Vil’yams – reference: DeinekaVSSergienkoIVSkopetskyVVModels and Methods to Solve Problems with Interface Conditions [in Russian]1998KyivNaukova Dumka – reference: NomirovskiiDAApproximate method for solving the boundary-value problem for a parabolic equation with inhomogeneous transmission conditions of nonideal contact typeComputational Mathematics and Mathematics Physics20064669951006228536410.1134/S096554250606008X – reference: DemchenkoVFKrivtsunIVPavlykVODiltheyULisnyiOBNakvasyukVVProblems of heat, mass and charge transfer with discontinuous solutionsEuropean J. of Applied Math.2011224365380281291710.1017/S095679251100012X1227.35129 – reference: KlyushinDALyashkoSINomirovskiiDAPetuninYISemenovVVGeneralized Solutions of Operator Equations and Extreme Elements2012New YorkSpringer10.1007/978-1-4614-0619-81240.47002 – reference: Fumio Kikuchi, “Numerical analysis of a mixed finite element method for plate buckling problems,” Inst. of Space and Aeronautical Science, Univ. of Tokyo Report, No. 584, September, 165–190 (1980). – reference: SergienkoIVDeinekaVSSystems Analysis of Multicomponent Distributed Systems [in Russian]2009KyivNaukova Dumka1297.93076 – reference: MercierBOsbornJRappazJRaviartPAEigenvalue approximation by mixed and hybrid methodsMathematics of Computation19813615442745360650510.1090/S0025-5718-1981-0606505-90472.65080 – reference: LyashkoIIDemchenkoVFGeneralized statements of problems of heat and mass transfer in layered media1987KyivPrepr. AN UkrSSR, V. M. Glushkov Inst. of Cybernetics – reference: SemenovVVSolvability of a parabolic transmission problem with the condition of a generalized proper lumped sourceDifferential Equations2005416878886220579210.1007/s10625-005-0227-x1086.35020 – volume: 41 start-page: 878 issue: 6 year: 2005 ident: 9895_CR3 publication-title: Differential Equations doi: 10.1007/s10625-005-0227-x – volume-title: Generalized Solutions of Operator Equations and Extreme Elements year: 2012 ident: 9895_CR10 doi: 10.1007/978-1-4614-0619-8 – volume-title: Models and Methods to Solve Problems with Interface Conditions [in Russian] year: 1998 ident: 9895_CR2 – volume: 40 start-page: 1467 issue: 10 year: 2004 ident: 9895_CR7 publication-title: Diff. Uravn. – ident: 9895_CR11 – volume: 36 start-page: 427 issue: 154 year: 1981 ident: 9895_CR12 publication-title: Mathematics of Computation doi: 10.1090/S0025-5718-1981-0606505-9 – volume: 46 start-page: 995 issue: 6 year: 2006 ident: 9895_CR4 publication-title: Computational Mathematics and Mathematics Physics doi: 10.1134/S096554250606008X – volume-title: Systems Analysis of Multicomponent Distributed Systems [in Russian] year: 2009 ident: 9895_CR1 – volume-title: Generalized statements of problems of heat and mass transfer in layered media year: 1987 ident: 9895_CR5 – volume: 233 start-page: 1 issue: 1 year: 2007 ident: 9895_CR8 publication-title: J. of Differential Equations doi: 10.1016/j.jde.2006.09.025 – volume: 22 start-page: 365 issue: 4 year: 2011 ident: 9895_CR6 publication-title: European J. of Applied Math. doi: 10.1017/S095679251100012X – volume-title: Hilbert’s 20th Problem. Generalized Solutions of Functional Equations [in Russian] year: 2009 ident: 9895_CR9
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Snippet	We study a linear parabolic system in a domain with a thin low-permeable inclusion. A new formulation of the problem is obtained with unknowns (u, ω). Under... We study a linear parabolic system in a domain with a thin low-permeable inclusion. A new formulation of the problem is obtained with unknowns (u, [omega]).... We study a linear parabolic system in a domain with a thin low-permeable inclusion. A new formulation of the problem is obtained with unknowns (u, omega )....
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SubjectTerms	Analysis Artificial Intelligence Control Cybernetics Differential equations Heat transfer Inclusions Materials science Mathematical analysis Mathematical models Mathematics Mathematics and Statistics Partial differential equations Processor Architectures Software Engineering/Programming and Operating Systems Studies Systems analysis Systems Theory Transport processes Transportation models
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Title	Generalized Statements and Properties of Models of Transport Processes in Domains with Cuts
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