Global existence and large time asymptotic bounds of solutions of thermal diffusive combustion systems on
P. Collet, J. Xin (1996)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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P. Collet, J. Xin (1996)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Piotr Biler, Grzegorz Karch, Wojbor A Woyczyński (2001)
Annales de l'I.H.P. Analyse non linéaire
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Pierre Louis Lions, Giuseppe Toscani (1997)
Revista Matemática Iberoamericana
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We investigate, in the diffusive scaling, the limit to the macroscopic description of finite-velocity Boltzmann kinetic models, where the rate coefficient in front of the collision operator is assumed to be dependent of the mass density. It is shown that in the limit the flux vanishes, while the evolution of the mass density is governed by a nonlinear parabolic equation of porous medium type. In the last part of the paper we show that our method adapts to prove the so-called Rosseland...
Razvan Gabriel Iagar, Juan Luis Vázquez (2009)
Annales de l'I.H.P. Analyse non linéaire
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Engler, Hans (2010)
International Journal of Differential Equations
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Piotr Biler, Grzegorz Karch (2000)
Annales Polonici Mathematici
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We study solutions to a nonlinear parabolic convection-diffusion equation on the half-line with the Neumann condition at x=0. The analysis is based on the properties of self-similar solutions to that problem.
Miguel A. Herrero, Juan J. L. Velazquez (1997)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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