Díaz Díaz, Jesús Ildefonso and Antontsev, S.N.
(2008)
*Mathematical treatment of the discharge of a laminar hot gas in a stagnant colder atmosphere.*
Journal of applied mechanics and technical physics, 49
(4).
pp. 681-692.
ISSN 0021-8944

PDF
Restringido a Repository staff only hasta 31 December 2020. 183kB |

Official URL: http://www.springerlink.com/content/a227t01x326535qt/fulltext.pdf

## Abstract

We study the boundary-layer approximation of the classical mathematical model that, describes the discharge of a, laminar hot gas in a stagnant colder atmosphere of the same gas. We prove the existence and uniqueness of solutions to a nondegenerate problem. (without, zones of stagnation of gas temperature or velocity). The asymptotic behavior of these solutions is also studied.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | diffusion; model; heat; systems of nonlinear degenerate parabolic equations; diffusion coupling; temperature gas jets; asymptotic behavior |

Subjects: | Sciences > Mathematics > Differential equations |

ID Code: | 15198 |

References: | S. N. Antontsev and J. I. Díaz, “Mathematical analysis of the discharge of a laminar hot gas in a colder atmosphere,” in: Differential Equations and Related Topics, Book of Abstr. Int. Conf., Moscow State Univ., Moscow (2007), pp. 19–20. S. N. Antontsev and J. I. Díaz, “Mathematical analysis of the discharge of a laminar hot gas in a colder atmosphere,” Revista Real Acad. Cien. Exact., Ser. Appl. Math., 101, No. 1, 119–124 (2007). S. N. Antontsev and J. I. Díaz, “On thermal and stagnation interfaces generated by the discharge of a laminar hot gas in a stagnant colder atmosphere,” Prepiblications of the Departamento de Matematica Aplicada of the UCM (2008). S. Pai, Fluid Dynamics of Jets, D. Van Nostrand Comp., Inc., Toronto-New York-London (1954). S. Pai, “Two-dimensional jet mixing of a compressible fluid,” J. Aeronaut. Sci., 16, 463–469 (1949). S. Pai, “Axially symmetrical jet mixing of a compressible fluid,” Quart. Appl. Math., 10, 141–148 (1952). M. Sánchez-Sanz, A. Sánchez, and A. Liñán, “Front solutions in high-temperature laminar gas jets,” J. Fluid Mech., 547, 257–266 (2006). L. Chen and A. Jungel, “Analysis of a parabolic cross-diffusion population model without self-diffusion,” J. Differ. Eq., 224, No. 1, 39–59 (2006). L. Chen and A. Jungel, “Analysis of a parabolic cross-diffusion semiconductor model with electron-hole scattering,” Comm. Partial. Differ. Eq., 32, Nos. 1/3, 127–148 (2007). A. Hill, “Double-diffusive convection in a porous medium with a concentration based internal heat source,” Proc. Roy. Soc. London, Ser. A, 461, No. 2054, 561–574 (2005). R. Shepherd and R. J. Wiltshire, “An analytical approach to coupled heat and moisture transport in soil,” Transport Porous Media, 20, No. 3, 281–304 (1995). S. N. Antontsev, J. I. Díaz, and S. Shmarev, “Energy methods for free boundary problems: Applications to non-linear PDEs and fluid mechanics,” in: Progress in Nonlinear Differential Equations and Their Applications, Vol. 48, Birkhäuser Boston, Inc., Boston (2002). G. I. Barenblatt and M. I. Vishik, “On finite velocity of propagation of nonstationary filtration of a liquid or gas,” Prikl. Mat. Mekh., 20, 411–417 (1956). J. L. Vázquez, “An introduction to the mathematical theory of the porous medium equation,” in: Shape Optimization and Free Boundaries (Montreal, 1990), NATO Adv. Sci. Inst., Ser. C: Math. Phys. Sci., Vol. 380, Kluwer Acad. Publ., Dordrecht (1992), pp. 347–389. J. L. Vázquez, “Smoothing and decay estimates for nonlinear diffusion equations. Equations of porous medium type,” in: Lecture Series in Mathematics and Its Applications, Vol. 33, Oxford Univ. Press, Oxford (2006). J. L. Vázquez, The Porous Medium Equation. Mathematical Theory, Oxford Mathematical monographs, The Clarendon Press-Oxford Univ. Press, Oxford (2007). Y. B. Zeldovič and A. S. Kompaneec, “On the theory of propagation of heat with the heat conductivity depending upon the temperature,” in: Collection in Honor of the 70th Birthday of Acad. A. F. Yoffe [in Russian], Izdat. Akad. Nauk SSSR, Moscow (1950), pp. 61–71. O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural’tseva, Linear and Quasi-Linear Equations of Parabolic Type, Am. Math. Soc., Providence (1967); translated from Russian by S. Smith, Translations of Mathematical Monographs, Vol. 23. P. Bénilan and S. N. Kruzhkov, “Conservation laws with continuos flux function,” Nonlinear Differ. Eq. Appl., 3, No. 4, 395–419 (1996). S. N. Kruzhkov, “First-order quasilinear equations in several independent variables,” Mat. Sb., 81, No. 123, 228–255 (1970). |

Deposited On: | 11 May 2012 07:39 |

Last Modified: | 06 Feb 2014 10:18 |

Repository Staff Only: item control page