A nonlinear degenerate parabolic equation
B. H. Gilding (1977)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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B. H. Gilding (1977)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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D. G. Aronson (1968)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Tber, Moulay Hicham (2007)
APPS. Applied Sciences
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J. Naumann, J. Wolf (1997)
Rendiconti del Seminario Matematico della Università di Padova
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B. H. Gilding, L. A. Peletier (1981)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Bjorn E. J. Dahlberg, Carlos E. Kenig (1986)
Revista Matemática Iberoamericana
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The purpose of this paper is to study nonnegative solutions u of the nonlinear evolution equations ∂u/∂t = Δφ(u), x ∈ Rn, 0 < t < T ≤ +∞ (1.1) Here the nonlinearity φ is assumed to be continuous, increasing with φ(0) = 0. This equation arises in various physical problems, and specializing φ leads to models for nonlinear filtrations, or for the gas flow in a porous medium. For a recent survey in these...
J. Naumann (1990)
Rendiconti del Seminario Matematico della Università di Padova
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Y. Amirat, A. Ziani (2004)
Bollettino dell'Unione Matematica Italiana
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We show the solvability of a nonlinear degenerate parabolic system of two equations describing the displacement of one compressible fluid by another, completely miscible with the first, in a one-dimensional porous medium, neglecting the molecular diffusion. We use the technique of renormalised solutions for parabolic equations in the derivation of a priori estimates for viscosity type solutions. We pass to the limit, as the molecular diffusion coefficient tends to 0, on the parabolic...