Displaying similar documents to “Continuity of solutions of the porous media equation”

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...

Non-negative solutions to fast diffusions.

Bjorn E. J. Dahlberg, Carlos E. Kenig (1988)

Revista Matemática Iberoamericana

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The purpose of this work is to study the class of non-negative continuous weak solutions of the non-linear evolution equation ∂u/∂t = ∆φ(u),   x ∈ Rn, 0 < t < T ≤ +∞.