Displaying similar documents to “Uniqueness of the boundary behavior for large solutions to a degenerate elliptic equation involving the ∞-Laplacian.”

The waiting time property for parabolic problems trough the nondiffusion of support for the stationary problems.

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.

Interfaces in solutions of diffusion-absorption equations.

Sergei Shmarev (2002)

RACSAM

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We study the properties of interfaces in solutions of the Cauchy problem for the nonlinear degenerate parabolic equation u = Δu - u in R x (0,T] with the parameters m > 1, p > 0 satisfying the condition m + p ≥ 2. We show that the velocity of the interface Γ(t) = ∂{supp u(x,t)} is given by the formula v = [ -m / (m-1) ∇u + ∇Π ]| where Π is the solution of the degenerate elliptic equation div (u∇Π) + u = 0, Π = 0 on Γ(t). We give explicit formulas which represent the interface...

Boundary trace of positive solutions of nonlinear elliptic inequalities

Moshe Marcus, Laurent Véron (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We develop a new method for proving the existence of a boundary trace, in the class of Borel measures, of nonnegative solutions of - Δ u + g ( x , u ) 0 in a smooth domain Ω under very general assumptions on g . This new definition which extends the previous notions of boundary trace is based upon a sweeping technique by solutions of Dirichlet problems with measure boundary data. We also prove a boundary pointwise blow-up estimate of any solution of such inequalities in terms of the Poisson kernel. If the...

Explosive solutions of semilinear elliptic systems with gradient term.

Marius Ghergu, Vicentiu Radulescu (2003)

RACSAM

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Estudiamos la existencia de soluciones del sistema elíptico no lineal Δu + |∇u| = p(|x|)f(v), Δv + |∇v| = q(|x|)g(u) en Ω que explotan en el borde. Aquí Ω es un dominio acotado de R o el espacio total. Las nolinealidades f y g son funciones continuas positivas mientras que los potenciales p y q son funciones continuas que satisfacen apropiadas condiciones de crecimiento en el infinito. Demostramos que las soluciones explosivas en el borde dejan de existir si f y g son sublineales. Esto...