Mathematical Models of Combustion Processes
In this paper, we consider model problems of chemical kinetics that lead to singularly perturbed parabolic equations in domains with nonsmooth boundaries. The solvability of such problems depends on the properties of the inhomogeneity at corner points of the boundary.
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| Published in | Journal of mathematical sciences (New York, N.Y.) Vol. 281; no. 3; pp. 390 - 397 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Cham
Springer International Publishing
10.05.2024
Springer Springer Nature B.V |
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| Abstract | In this paper, we consider model problems of chemical kinetics that lead to singularly perturbed parabolic equations in domains with nonsmooth boundaries. The solvability of such problems depends on the properties of the inhomogeneity at corner points of the boundary. |
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| AbstractList | In this paper, we consider model problems of chemical kinetics that lead to singularly perturbed parabolic equations in domains with nonsmooth boundaries. The solvability of such problems depends on the properties of the inhomogeneity at corner points of the boundary. In this paper, we consider model problems of chemical kinetics that lead to singularly perturbed parabolic equations in domains with nonsmooth boundaries. The solvability of such problems depends on the properties of the inhomogeneity at corner points of the boundary. Keywords and phrases: boundary layer, singularly perturbed equation, asymptotic approximation. AMS Subject Classification: 34E10 |
| Audience | Academic |
| Author | Denisov, I. V. Denisov, A. I. |
| Author_xml | – sequence: 1 givenname: I. V. surname: Denisov fullname: Denisov, I. V. email: den_tspu@mail.ru organization: Tula State Pedagogical University – sequence: 2 givenname: A. I. surname: Denisov fullname: Denisov, A. I. organization: National Research University Higher School of Economics |
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| Cites_doi | 10.1512/iumj.1972.21.21012 10.1512/iumj.1972.21.21079 10.1016/B978-0-12-165550-1.50007-0 |
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| Copyright | The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. COPYRIGHT 2024 Springer |
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| Keywords | Singularly perturbed equation Asymptotic approximation 34E10 Boundary layer |
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| References | CR2 Denisov (CR7) 2019; 1 Vasilieva, Butuzov (CR9) 1990 Denisov (CR5) 2017; 2 Sattinger (CR8) 1972; 11 Denisov (CR4) 1996; 10 Butuzov (CR3) 1972; 3 Vishik, Lyusternik (CR10) 1957; 5 Denisov (CR6) 2018; 4 Amann (CR1) 1971; 2 IV Denisov (7113_CR4) 1996; 10 DH Sattinger (7113_CR8) 1972; 11 IV Denisov (7113_CR5) 2017; 2 AB Vasilieva (7113_CR9) 1990 H Amann (7113_CR1) 1971; 2 7113_CR2 MI Vishik (7113_CR10) 1957; 5 IV Denisov (7113_CR7) 2019; 1 IV Denisov (7113_CR6) 2018; 4 VF Butuzov (7113_CR3) 1972; 3 |
| References_xml | – volume: 3 start-page: 582 year: 1972 end-page: 597 ident: CR3 article-title: Asymptotics of solutions of a difference equation with a small parameter in a rectangular domain publication-title: Zh. Vychisl. Mat. Mat. Fiz. – volume: 1 start-page: 102 year: 2019 end-page: 117 ident: CR7 article-title: Angular boundary layers in boundary-value problems for singularly perturbed parabolic equations with nonlinearities publication-title: Zh. Vychisl. Mat. Mat. Fiz. – volume: 2 start-page: 125 year: 1971 end-page: 125 ident: CR1 article-title: On the existence of positive solutions of nonlinear elliptic boundary-value problems publication-title: Indiana Univ. Math. J. doi: 10.1512/iumj.1972.21.21012 – volume: 4 start-page: 1 year: 2018 end-page: 11 ident: CR6 article-title: Angular boundary layers in boundary-value problems for singularly perturbed parabolic equations with monotonic nonlinearities publication-title: Zh. Vychisl. Mat. Mat. Fiz. – volume: 2 start-page: 255 year: 2017 end-page: 274 ident: CR5 article-title: Angular boundary layers in boundary-value problems for singularly perturbed parabolic equations with quadratic nonlinearities publication-title: Zh. Vychisl. Mat. Mat. Fiz. – ident: CR2 – volume: 11 start-page: 979 year: 1972 end-page: 1000 ident: CR8 article-title: Monotone methods in nonlinear elliptic and parabolic boundary-value problems publication-title: Indiana Univ. Math. J. doi: 10.1512/iumj.1972.21.21079 – volume: 10 start-page: 56 year: 1996 end-page: 72 ident: CR4 article-title: First boundary-value problem for a quasilinear singularly perturbed parabolic equation in a rectangle publication-title: Zh. Vychisl. Mat. Mat. Fiz. – year: 1990 ident: CR9 publication-title: Asymptotic Methods in the Theory of Singular Perturbations – volume: 5 start-page: 3 year: 1957 end-page: 122 ident: CR10 article-title: Regular degeneration and boundary layer for linear differential equations with small parameters publication-title: Usp. Mat. Nauk – volume: 2 start-page: 255 year: 2017 ident: 7113_CR5 publication-title: Zh. Vychisl. Mat. Mat. Fiz. – ident: 7113_CR2 doi: 10.1016/B978-0-12-165550-1.50007-0 – volume: 3 start-page: 582 year: 1972 ident: 7113_CR3 publication-title: Zh. Vychisl. Mat. Mat. Fiz. – volume-title: Asymptotic Methods in the Theory of Singular Perturbations year: 1990 ident: 7113_CR9 – volume: 5 start-page: 3 year: 1957 ident: 7113_CR10 publication-title: Usp. Mat. Nauk – volume: 2 start-page: 125 year: 1971 ident: 7113_CR1 publication-title: Indiana Univ. Math. J. doi: 10.1512/iumj.1972.21.21012 – volume: 4 start-page: 1 year: 2018 ident: 7113_CR6 publication-title: Zh. Vychisl. Mat. Mat. Fiz. – volume: 1 start-page: 102 year: 2019 ident: 7113_CR7 publication-title: Zh. Vychisl. Mat. Mat. Fiz. – volume: 10 start-page: 56 year: 1996 ident: 7113_CR4 publication-title: Zh. Vychisl. Mat. Mat. Fiz. – volume: 11 start-page: 979 year: 1972 ident: 7113_CR8 publication-title: Indiana Univ. Math. J. doi: 10.1512/iumj.1972.21.21079 |
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| SubjectTerms | Analysis Chemical reaction, Rate of Combustion Inhomogeneity Mathematics Mathematics and Statistics Reaction kinetics |
| Title | Mathematical Models of Combustion Processes |
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