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Displaying similar documents to “Non-negative solutions to fast diffusions.”

Non-negative solutions of generalized porous medium equations.

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...

Global weak solutions for a degenerate parabolic system modelling a one-dimensional compressible miscible flow in porous media

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...