Refined asymptotic expansions for nonlocal diffusion equations
We study the asymptotic behavior for solutions to nonlocal diffusion models of the form u t = J*u - u in the whole ℝ with an initial condition u(x, 0) = u 0(x). Under suitable hypotheses on J (involving its Fourier transform) and u 0, it is proved an expansion of the form equation is presented where...
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2008
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14243199_v8_n4_p617_Ignat http://hdl.handle.net/20.500.12110/paper_14243199_v8_n4_p617_Ignat |
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| Sumario: | We study the asymptotic behavior for solutions to nonlocal diffusion models of the form u t = J*u - u in the whole ℝ with an initial condition u(x, 0) = u 0(x). Under suitable hypotheses on J (involving its Fourier transform) and u 0, it is proved an expansion of the form equation is presented where K t is the regular part of the fundamental solution and the exponent A depends on J, q, k and the dimension d. Moreover, we can obtain bounds for the difference between the terms in this expansion and the corresponding ones for the expansion of the evolution given by fractional powers of the Laplacian, ν-t (x, t) = -(-Δ) 2ν (x, t). © 2008 Birkhaueser. |
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