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Abstract:

In this paper we study the nonlocal p-Laplacian- type diffusion equation ut(t,x) = ∫RN J(x-y)|u(t, y) -u(t,x)| p-2(u(t, y) -u(t,x)) dy, (t, x) ∈]0,T[×ω, with u(t, x) = ψ(x) for (t, x) ∈ ]0,T[×(RN\\ω). If p > 1, this is the nonlocal analogous problem to the well-known local p- Laplacian evolution equation ut = div(| δu|p-2 δu) with Dirichlet boundary condition u(t, x) =ψ(x) on (t, x) ∈ ]0,T[×∂ω. If p = 1, this is the nonlocal analogous to the total variation flow. When p = +∞ (this has to be interpreted as the limit as p → +∞ in the previous model) we find an evolution problem that can be seen as a nonlocal model for the formation of sandpiles (here u(t,x) stands for the height of the sandpile) with prescribed height of sand outside of ω. We prove, as main results, existence, uniqueness, a contraction property that gives well posedness of the problem, and the convergence of the solutions to solutions of the local analogous problem when a rescaling parameter goes to zero. © 2009 Society for Industrial and Applied Mathematics.

Registro:

Documento: Artículo
Título:A nonlocal p-laplacian evolution equation with nonhomogeneous dirichlet boundary conditions
Autor:Andreu, F.; Mazón, J.M.; Rossi, J.D.; Toledo, J.
Filiación:Departament de Matemàtica Aplicada, Universitat de València, Valencia, Spain
Departament d'Anàlisi Matemàtica, Universitat de València, Valencia, Spain
IMDEA Matematicas, C-IX, Campus Cantoblanco UAM, Madrid, Spain
Dpto. de Matemáticas, FCEyN Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
Palabras clave:Nonhomogeneous Dirichlet boundary conditions; Nonlocal diffusion; P-Laplacian; Sandpiles; Total variation flow; Nonhomogeneous Dirichlet boundary conditions; Nonlocal diffusion; P-Laplacian; Sandpiles; Total variation flow; Boundary conditions; Diffusion; Laplace transforms; Sand
Año:2009
Volumen:40
Número:5
Página de inicio:1815
Página de fin:1851
DOI: http://dx.doi.org/10.1137/080720991
Título revista:SIAM Journal on Mathematical Analysis
Título revista abreviado:SIAM J. Math. Anal.
ISSN:00361410
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00361410_v40_n5_p1815_Andreu

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Citas:

---------- APA ----------
Andreu, F., Mazón, J.M., Rossi, J.D. & Toledo, J. (2009) . A nonlocal p-laplacian evolution equation with nonhomogeneous dirichlet boundary conditions. SIAM Journal on Mathematical Analysis, 40(5), 1815-1851.
http://dx.doi.org/10.1137/080720991
---------- CHICAGO ----------
Andreu, F., Mazón, J.M., Rossi, J.D., Toledo, J. "A nonlocal p-laplacian evolution equation with nonhomogeneous dirichlet boundary conditions" . SIAM Journal on Mathematical Analysis 40, no. 5 (2009) : 1815-1851.
http://dx.doi.org/10.1137/080720991
---------- MLA ----------
Andreu, F., Mazón, J.M., Rossi, J.D., Toledo, J. "A nonlocal p-laplacian evolution equation with nonhomogeneous dirichlet boundary conditions" . SIAM Journal on Mathematical Analysis, vol. 40, no. 5, 2009, pp. 1815-1851.
http://dx.doi.org/10.1137/080720991
---------- VANCOUVER ----------
Andreu, F., Mazón, J.M., Rossi, J.D., Toledo, J. A nonlocal p-laplacian evolution equation with nonhomogeneous dirichlet boundary conditions. SIAM J. Math. Anal. 2009;40(5):1815-1851.
http://dx.doi.org/10.1137/080720991