The dipole solution for the porous medium equation in several space dimensions
Josephus Hulshof, Juan Luis Vazquez (1993)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Josephus Hulshof, Juan Luis Vazquez (1993)
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...
Fernando Quirós, Juan Luis Vazquez (1999)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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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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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 (Rn x (0,T)) to (0.1) ut - 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...
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,...
Tadeusz Śliwa (1980)
Colloquium Mathematicae
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