Geodesic
Mathematical models of combustion processes
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the All-Russian Scientific Conference «Differential Equations and Their Applications» dedicated to the 85th anniversary of Professor M.T.Terekhin. Ryazan State University named for S.A. Yesenin, Ryazan, May 17-18, 2019. Part 1, Tome 185 (2020), pp. 50-57.

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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: boundary layer, singularly perturbed equation, asymptotic approximation. 
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I. V. Denisov; A. I. Denisov. Mathematical models of combustion processes. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the All-Russian Scientific Conference «Differential Equations and Their Applications» dedicated to the 85th anniversary of Professor M.T.Terekhin. Ryazan State University named for S.A. Yesenin, Ryazan, May 17-18, 2019. Part 1, Tome 185 (2020), pp. 50-57. http://geodesic.mathdoc.fr/item/INTO_2020_185_a5/

[2] Butuzov V. F., “Asimptotika resheniya raznostnogo uravneniya s malymi shagami v pryamougolnoi oblasti”, Zh. vychisl. mat. mat. fiz., 3 (1972), 582–597 | MR

[3] Vasileva A. B., Butuzov V. F., Asimptoticheskie metody v teorii singulyarnykh vozmuschenii, Vysshaya shkola, M., 1990 | MR

[4] Vishik M. I., Lyusternik L. A., “Regulyarnoe vyrozhdenie i pogranichnyi sloi dlya lineinykh differentsialnykh uravnenii s malym parametrom”, Usp. mat. nauk., 5 (1957), 3–122 | Zbl

[5] Denisov I. V., “Pervaya kraevaya zadacha dlya kvazilineinogo singulyarno vozmuschennogo parabolicheskogo uravneniya v pryamougolnike”, Zh. vychisl. mat. mat. fiz., 10 (1996), 56–72 | Zbl

[6] Denisov I. V., “Uglovoi pogranichnyi sloi v kraevykh zadachakh dlya singulyarno vozmuschennykh parabolicheskikh uravnenii s kvadratichnoi nelineinostyu”, Zh. vychisl. mat. mat. fiz., 2 (2017), 255–274 | Zbl

[7] Denisov I. V., “Uglovoi pogranichnyi sloi v kraevykh zadachakh dlya singulyarno vozmuschennykh parabolicheskikh uravnenii s monotonnoi nelineinostyu”, Zh. vychisl. mat. mat. fiz., 4 (2018), 1–11

[8] Denisov I. V., “Uglovoi pogranichnyi sloi v kraevykh zadachakh dlya singulyarno vozmuschennykh parabolicheskikh uravnenii s nelineinostyami”, Zh. vychisl. mat. mat. fiz., 1 (2019), 102–117 | Zbl

[9] Amann H., “On the existence of positive solutions of nonlinear elliptic boundary-value problems”, Indiana Univ. Math. J., 2 (1971), 125–125 | DOI | MR

[10] Amann H., “Periodic solutions of semilinear parabolic equations”, Nonlinear Analysis: Collections of Papers in Honor of Erich Rothe, Academic Press, New York, 1978, 1–29 | MR

[11] Sattinger D. H., “Monotone methods in nonlinear elliptic and parabolic boundary-value problems”, Indiana Univ. Math. J., 11 (1972), 979–1000 | DOI | MR