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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Detalles Bibliográficos
Autor principal: Rossi, Julio Daniel
Publicado: 2008
Materias:
Asymptotic behaviour
Neumann boundary conditions
Nonlocal diffusion
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14243199_v8_n1_p189_Andreu
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
id paper:paper_14243199_v8_n1_p189_Andreu
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spelling paper:paper_14243199_v8_n1_p189_Andreu2023-06-08T16:13:50Z The Neumann problem for nonlocal nonlinear diffusion equations Rossi, Julio Daniel 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. 2008 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14243199_v8_n1_p189_Andreu 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
Rossi, Julio Daniel
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.
author Rossi, Julio Daniel
author_facet Rossi, Julio Daniel
author_sort Rossi, Julio Daniel
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
publishDate 2008
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14243199_v8_n1_p189_Andreu
http://hdl.handle.net/20.500.12110/paper_14243199_v8_n1_p189_Andreu
work_keys_str_mv AT rossijuliodaniel theneumannproblemfornonlocalnonlineardiffusionequations
AT rossijuliodaniel neumannproblemfornonlocalnonlineardiffusionequations
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