Non-negative solutions of generalized porous medium equations.

Bjorn E. J. Dahlberg; Carlos E. Kenig

Displaying similar documents to “Non-negative solutions of generalized porous medium equations.”

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 ≤ +∞.

Initial traces of solutions to a one-phase Stefan problem in an infinite strip.

Daniele Andreucci, Marianne K. Korten (1993)

Revista Matemática Iberoamericana

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The main result of this paper is an integral estimate valid for non-negative solutions (with no reference to initial data) u ∈ L¹ _loc (R_n x (0,T)) to (0.1) u_t - Δ(u - 1)₊ = 0, in D'(Rⁿ x (0,T)), for T > 0, n ≥ 1. Equation (0.1) is a formulation of a one-phase Stefan problem: in this connection...

Uniqueness and existence of solution in the BV(Q) space to a doubly nonlinear parabolic problem.

Jesús Ildefonso Díaz, Juan Francisco Padial (1996)

Publicacions Matemàtiques

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In this paper we present some results on the uniqueness and existence of a class of weak solutions (the so called BV solutions) of the Cauchy-Dirichlet problem associated to the doubly nonlinear diffusion equation b(u)_t - div (|∇u - k(b(u))e|^p-2 (∇u - k(b(u))e)) + g(x,u) = f(t,x). This problem arises in the study of some turbulent regimes: flows of incompressible turbulent fluids through porous media, gases flowing in pipelines,...

On the Cauchy problem and initial traces for a class of evolution equations with strongly nonlinear sources

D. Andreucci, E. Di Benedetto (1991)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Fundamental solutions and asymptotic behaviour for the p-Laplacian equation.

Soshana Kamin, Juan Luis Vázquez (1988)

Revista Matemática Iberoamericana

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We establish the uniqueness of fundamental solutions to the p-Laplacian equation u_t = div (|Du|^p-2 Du), p > 2, defined for x ∈ R^N, 0 < t < T. We derive from this result the asymptotic behavoir of nonnegative solutions with finite mass, i.e., such that u(*,t) ∈ L¹(R^N). Our methods also apply to the porous medium equation u_t...

Continuity of solutions of the porous media equation

B. H. Gilding, L. A. Peletier (1981)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Nonsteady flow of water and oil through inhomogeneous porous media

H. W. Alt, E. Di Benedetto (1985)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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The relation between the porous medium and the eikonal equations in several space dimensions.

Pierre-Louis Lions, Panagiotis E. Souganidis, Juan Luis Vázquez (1987)

Revista Matemática Iberoamericana

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We study the relation between the porous medium equation u_t = Δ(u^m), m > 1, and the eikonal equation v_t = |Dv|². Under quite general assumtions, we prove that the pressure and the interface of the solution of the Cauchy problem for the porous medium equation converge as m↓1 to the viscosity solution and the interface of the Cauchy problem for the eikonal equation. We also address the same...