Supersolutions and stabilization on the solution of a nonlinear parabolic system.
Hamid Elouardi, François De Thélin (1989)
Publicacions Matemàtiques
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Hamid Elouardi, François De Thélin (1989)
Publicacions Matemàtiques
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Robert Dalmasso (1995)
Revista Matemática Iberoamericana
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In this paper we discuss the uniqueness of positive solutions of the nonlinear second order system -u'' = g(v), -v'' = f(u) in (-R,R), u(±R) = v(±R) = 0 where f and g satisfy some appropriate conditions. Our result applies, in particular, to g(v) = v, f(u) = u, p > 1, or f(u) = λu + au + ... + au, with p > 1, a > 0 for j = 1, ..., k and 0 ≤ λ < μ where μ = π/4R.
D. G. Aronson, James Serrin (1967)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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S. Kamin, L. A. Peletier (1985)
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...
Santos, Lisa (1991)
Portugaliae mathematica
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Luis Alvarez, Jesús Ildefonso Díaz (2003)
RACSAM
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In this note we study the waiting time phenomenon for local solutions of the nonlinear diffusion equation through its connection with the nondiffusion of the support property for local solutions of the family of discretized elliptic problems. We show that, under a suitable growth condition on the initial datum near the boundary of its support, a finite part of the family of solutions of the discretized problem maintain unchanged its support.
Vázquez, Juan L. (1982)
Portugaliae mathematica
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