Díaz Díaz, Jesús Ildefonso and Antontsev, S.N.
(2007)
*Mathematical analysis of the discharge of a laminar hot gas in a colder atmosphere.*
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A: Matemáticas , 101
(1).
pp. 119-124.
ISSN 1578-7303

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## Abstract

We study the boundary layer approximation of the, already classical, mathematical model which describes the discharge of a laminar hot gas in a stagnant colder atmosphere of the same gas. We start by proving the existence and uniqueness of solutions of the nondegenerate problem under assumptions implying that the temperature T and the horizontal velocity u of the gas are strictly positive: T >= delta > 0 and u > epsilon > 0 (here delta and epsilon are given as boundary conditions in the external atmosphere). We also study the limit cases delta = 0 or epsilon = 0 in which the governing system of equations become degenerate. We show that in those cases it appear some interfaces separating the zones where T and U are positive from those where they vanish.

Item Type: | Article |
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Uncontrolled Keywords: | gas dynamics, localization effects, boundary layer approximation, non isothermal laminar gas jets, nonlinear PDEs |

Subjects: | Sciences > Mathematics > Differential equations |

ID Code: | 15292 |

References: | Antontsev, S. N. and Díaz, J. I., (2007). On thermal and stagnation interfaces generated by the discharge of a laminar hot gas in a stagnant colder atmosphere, Manuscript. To appear. Antontsev, S. N., Díaz, J. I. and Shmarev, S. I., (2002). Energy Methods for Free Boundary Problems: Applications to Non-linear PDEs and Fluid Mechanics, Bikhäuser, Boston, Progress in Nonlinear Differential Equations and Their Applications, Vol. 48. Barenblatt, G. I. and Višik, M. I., (1956). On finite velocity of propagation in problems of non-stationary filtration of a liquid or gas, Prikl. Mat. Meh., 20X, 411–417. Ladyženskaja, O. A., Solonnikov, V. A. and Ural'tseva, N. N., (1967). Linear and quasilinear equations of parabolic type, American Mathematical Society, Providence, R. I., Translated from the Russian by S. Smith. Translations of Mathematical Monographs, Vol. 23. Pai, S., (1952). Axially symmetrical jet mixing of a compressible fluid, Quart. Appl. Math., 10, 141–148. Pai, S., (1954). Fluid dynamics of jets, D. Van Nostrand Company, Inc., Toronto-New York-London. Sánchez-Sanz, M., Sánchez, A. and Li~nán, A., (2006). Front solutions in high-temperature laminar gas jets, J. Fluid. Mech., 547, 257–266. Vázquez, J. L., (1992). An introduction to the mathematical theory of the porous medium equation, in Shape Optimization and Free Boundaries, C, Mathematical and Physical Sciences, vol. 212 of Contemp. Math., Kluwer Acad. Publ., Dordrecht, Netherlands, 347–389. Zeldovič, Y. B. and Kompaneec, A. S., (1950). On the theory of propagation of heat with the heat conductivity depending upon the temperature, in Collection in honor of the seventieth birthday of academician A. F. Ioffe, Izdat. Akad. Nauk SSSR, Moscow, 61–71. |

Deposited On: | 21 May 2012 09:52 |

Last Modified: | 06 Feb 2014 10:21 |

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