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Abstract:

We study nonlocal diffusion models of the form (γ(u))_t (t, x) = \\int_{\\Omega} J(x-y)(u(t, y) - u(t, x))\\, dy. Here Ω is a bounded smooth domain andγ is a maximal monotone graph in {{R}}2. This is a nonlocal diffusion problem analogous with the usual Laplacian with Neumann boundary conditions. We prove existence and uniqueness of solutions with initial conditions in L 1 (Ω). Moreover, when γ is a continuous function we find the asymptotic behaviour of the solutions, they converge as t → ∞ to the mean value of the initial condition. © 2007 Birkhaueser.

Registro:

Documento: Artículo
Título:The Neumann problem for nonlocal nonlinear diffusion equations
Autor:Andreu, F.; Mazón, J.M.; Rossi, J.D.; Toledo, J.
Filiación:Departamento de Matemática Aplicada, Universitat de València, Valencia, Spain
Departamento de Análisis Matemático, Universitat de València, Valencia, Spain
Departamento de Matemática, FCEyN UBA (1428), Buenos Aires, Argentina
Palabras clave:Asymptotic behaviour; Neumann boundary conditions; Nonlocal diffusion
Año:2008
Volumen:8
Número:1
Página de inicio:189
Página de fin:215
DOI: http://dx.doi.org/10.1007/s00028-007-0377-9
Título revista:Journal of Evolution Equations
Título revista abreviado:J. Evol. Equ.
ISSN:14243199
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14243199_v8_n1_p189_Andreu

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Citas:

---------- APA ----------
Andreu, F., Mazón, J.M., Rossi, J.D. & Toledo, J. (2008) . The Neumann problem for nonlocal nonlinear diffusion equations. Journal of Evolution Equations, 8(1), 189-215.
http://dx.doi.org/10.1007/s00028-007-0377-9
---------- CHICAGO ----------
Andreu, F., Mazón, J.M., Rossi, J.D., Toledo, J. "The Neumann problem for nonlocal nonlinear diffusion equations" . Journal of Evolution Equations 8, no. 1 (2008) : 189-215.
http://dx.doi.org/10.1007/s00028-007-0377-9
---------- MLA ----------
Andreu, F., Mazón, J.M., Rossi, J.D., Toledo, J. "The Neumann problem for nonlocal nonlinear diffusion equations" . Journal of Evolution Equations, vol. 8, no. 1, 2008, pp. 189-215.
http://dx.doi.org/10.1007/s00028-007-0377-9
---------- VANCOUVER ----------
Andreu, F., Mazón, J.M., Rossi, J.D., Toledo, J. The Neumann problem for nonlocal nonlinear diffusion equations. J. Evol. Equ. 2008;8(1):189-215.
http://dx.doi.org/10.1007/s00028-007-0377-9