Abstract.
We study nonlocal diffusion models of the form
Here Ω is a bounded smooth domain andγ is a maximal monotone graph in \({\mathbb{R}}^2\). 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.
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Dedicated to I. Peral on the Occasion of His 60th Birthday
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Andreu, F., Mazón, J.M., Rossi, J.D. et al. The Neumann problem for nonlocal nonlinear diffusion equations. J. evol. equ. 8, 189–215 (2008). https://doi.org/10.1007/s00028-007-0377-9
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DOI: https://doi.org/10.1007/s00028-007-0377-9