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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2008
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| 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 |
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| Sumario: | 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. |
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