The Neumann problem for nonlocal nonlinear diffusion equations

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...

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Autores principales: Andreu, F., Mazón, J.M., Rossi, J.D., Toledo, J.
Formato: JOUR
Materias:
Asymptotic behaviour
Neumann boundary conditions
Nonlocal diffusion
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_14243199_v8_n1_p189_Andreu
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_14243199_v8_n1_p189_Andreu2023-10-03T16:13:34Z The Neumann problem for nonlocal nonlinear diffusion equations Andreu, F. Mazón, J.M. Rossi, J.D. Toledo, J. Asymptotic behaviour Neumann boundary conditions Nonlocal diffusion 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. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_14243199_v8_n1_p189_Andreu
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Asymptotic behaviour
Neumann boundary conditions
Nonlocal diffusion
spellingShingle Asymptotic behaviour
Neumann boundary conditions
Nonlocal diffusion
Andreu, F.
Mazón, J.M.
Rossi, J.D.
Toledo, J.
The Neumann problem for nonlocal nonlinear diffusion equations
topic_facet Asymptotic behaviour
Neumann boundary conditions
Nonlocal diffusion
description 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.
format JOUR
author Andreu, F.
Mazón, J.M.
Rossi, J.D.
Toledo, J.
author_facet Andreu, F.
Mazón, J.M.
Rossi, J.D.
Toledo, J.
author_sort Andreu, F.
title The Neumann problem for nonlocal nonlinear diffusion equations
title_short The Neumann problem for nonlocal nonlinear diffusion equations
title_full The Neumann problem for nonlocal nonlinear diffusion equations
title_fullStr The Neumann problem for nonlocal nonlinear diffusion equations
title_full_unstemmed The Neumann problem for nonlocal nonlinear diffusion equations
title_sort neumann problem for nonlocal nonlinear diffusion equations
url http://hdl.handle.net/20.500.12110/paper_14243199_v8_n1_p189_Andreu
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