Improved theory for a nonlinear degenerate parabolic equation
B. H. Gilding (1989)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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B. H. Gilding (1989)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Dominique Blanchard, Alessio Porretta (2001)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Abderrahmane El Hachimi, François De Thélin (1991)
Publicacions Matemàtiques
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In this paper we consider a nonlinear parabolic equation of the following type: (P) ∂u/∂t - div(|∇p|p-2 ∇u) = h(x,u) with Dirichlet boundary conditions and initial data in the case when 1 < p < 2. We construct supersolutions of (P), and by use of them, we prove that for tn → +∞, the solution of (P) converges to some solution of the elliptic equation associated with...
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...
B. H. Gilding (1977)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Thierry Goudon, Mazen Saad (2001)
Revista Matemática Iberoamericana
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This paper is devoted to general parabolic equations involving 0 and 1 order terms, in linear and nonlinear expressions, while the data only belong to L. Existence and entropic-uniqueness of solutions are proved.
Maurizio Badii (1994)
Publicacions Matemàtiques
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We consider the following quasilinear parabolic equation of degenerate type with convection term u = φ (u) + b(u) in (-L,0) x (0,T). We solve the associate initial-boundary data problem, with nonlinear flux conditions. This problem describes the evaporation of an incompressible fluid from a homogeneous porous media. The nonlinear condition in x = 0 means that the flow of fluid leaving the porous media depends on variable meteorological conditions and in a nonlinear manner on u. In x...