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Abstract:

In this paper we study the nonlocal p-Laplacian type diffusion equation,ut (t, x) = under(∫, Ω) J (x - y) | u (t, y) - u (t, x) |p - 2 (u (t, y) - u (t, x)) d y . If p > 1, this is the nonlocal analogous problem to the well-known local p-Laplacian evolution equation ut = div (| ∇ u |p - 2 ∇ u) with homogeneous Neumann boundary conditions. We prove existence and uniqueness of a strong solution, and if the kernel J is rescaled in an appropriate way, we show that the solutions to the corresponding nonlocal problems converge strongly in L∞ (0, T ; Lp (Ω)) to the solution of the p-Laplacian with homogeneous Neumann boundary conditions. The extreme case p = 1, that is, the nonlocal analogous to the total variation flow, is also analyzed. Finally, we study the asymptotic behavior of the solutions as t goes to infinity, showing the convergence to the mean value of the initial condition. © 2008 Elsevier Masson SAS. All rights reserved.

Registro:

Documento: Artículo
Título:A nonlocal p-Laplacian evolution equation with Neumann 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, Universitat Autonoma, C-IX, Madrid, Spain
Departamento de Matemática, FCEyN UBA, 1428 Buenos Aires, Argentina
Palabras clave:Neumann boundary conditions; Nonlocal diffusion; p-Laplacian; Total variation flow
Año:2008
Volumen:90
Número:2
Página de inicio:201
Página de fin:227
DOI: http://dx.doi.org/10.1016/j.matpur.2008.04.003
Título revista:Journal des Mathematiques Pures et Appliquees
Título revista abreviado:J. Math. Pures Appl.
ISSN:00217824
CODEN:JMPAA
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00217824_v90_n2_p201_Andreu.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00217824_v90_n2_p201_Andreu

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Citas:

---------- APA ----------
Andreu, F., Mazón, J.M., Rossi, J.D. & Toledo, J. (2008) . A nonlocal p-Laplacian evolution equation with Neumann boundary conditions. Journal des Mathematiques Pures et Appliquees, 90(2), 201-227.
http://dx.doi.org/10.1016/j.matpur.2008.04.003
---------- CHICAGO ----------
Andreu, F., Mazón, J.M., Rossi, J.D., Toledo, J. "A nonlocal p-Laplacian evolution equation with Neumann boundary conditions" . Journal des Mathematiques Pures et Appliquees 90, no. 2 (2008) : 201-227.
http://dx.doi.org/10.1016/j.matpur.2008.04.003
---------- MLA ----------
Andreu, F., Mazón, J.M., Rossi, J.D., Toledo, J. "A nonlocal p-Laplacian evolution equation with Neumann boundary conditions" . Journal des Mathematiques Pures et Appliquees, vol. 90, no. 2, 2008, pp. 201-227.
http://dx.doi.org/10.1016/j.matpur.2008.04.003
---------- VANCOUVER ----------
Andreu, F., Mazón, J.M., Rossi, J.D., Toledo, J. A nonlocal p-Laplacian evolution equation with Neumann boundary conditions. J. Math. Pures Appl. 2008;90(2):201-227.
http://dx.doi.org/10.1016/j.matpur.2008.04.003