Displaying similar documents to “Interfaces in solutions of diffusion-absorption equations.”

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.

Nonlinear nonlocal evolution problems.

N.-H. Chang, M. Chipot (2003)

RACSAM

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We consider a class of nonlinear parabolic problems where the coefficients are depending on a weighted integral of the solution. We address the issues of existence, uniqueness, stationary solutions and in some cases asymptotic behaviour.

Supersolutions and stabilization of the solutions of the equation∂u/∂t - div(|∇p| ∇u) = h(x,u), Part II.

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...

Uniqueness of the boundary behavior for large solutions to a degenerate elliptic equation involving the ∞-Laplacian.

Gregorio Díaz, Jesús Ildefonso Díaz (2003)

RACSAM

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En esta nota estimamos la tasa máxima de crecimiento en la frontera de las soluciones de viscosidad de -Δ∞u + λ|u|m-1u = f en Ω (λ > 0, m > 3). De hecho, mostramos que sólo hay una única tasa de explosión en la frontera para esas soluciones explosivas. También obtenemos una versión del Teorema de Liouville para el caso Ω = RN.

Analysis and numerical solution of a nonlinear cross-diffusion system arising in population dynamics.

Gonzalo Galiano, María Luisa Garzón, Ansgar Jüngel (2001)

RACSAM

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En este trabajo se estudia de modo analítico y numérico un problema en ecuaciones diferenciales en derivadas parciales que modela la dinámica de dos poblaciones afectadas por la presión poblacional inter e intraespecíficas y por un potencial medioambiental. Debido a los términos de difusión cruzada, el problema es fuertemente no lineal por lo que el principio del máximo y los métodos relacionados con el mismo no pueden ser aplicados. En primer lugar demostramos la existencia de soluciones...

Two problems in homogenization of porous media.

Jesús Ildefonso Díaz (1999)

Extracta Mathematicae

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The main goal of this work is to present two different problems arising in Fluid Dynamics of perforated domains or porous media. The first problem concerns the compressible flow of an ideal gas through a porous media and our goal is the mathematical derivation of Darcy's law. This is relevant in oil reservoirs, agriculture, soil infiltration, etc. The second problem deals with the incompressible flow of a fluid reacting with the exterior of many packed solid particles. This is related...