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...
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | JOUR |
| Materias: | |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_14243199_v8_n4_p617_Ignat |
| Aporte de: |
| id |
todo:paper_14243199_v8_n4_p617_Ignat |
|---|---|
| record_format |
dspace |
| spelling |
todo:paper_14243199_v8_n4_p617_Ignat2023-10-03T16:13:34Z Refined asymptotic expansions for nonlocal diffusion equations Ignat, L.I. Rossi, J.D. Asymptotic behavior Fractional Laplacian Nonlocal diffusion 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. 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_n4_p617_Ignat |
| 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 behavior Fractional Laplacian Nonlocal diffusion |
| spellingShingle |
Asymptotic behavior Fractional Laplacian Nonlocal diffusion Ignat, L.I. Rossi, J.D. Refined asymptotic expansions for nonlocal diffusion equations |
| topic_facet |
Asymptotic behavior Fractional Laplacian Nonlocal diffusion |
| description |
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. |
| format |
JOUR |
| author |
Ignat, L.I. Rossi, J.D. |
| author_facet |
Ignat, L.I. Rossi, J.D. |
| author_sort |
Ignat, L.I. |
| title |
Refined asymptotic expansions for nonlocal diffusion equations |
| title_short |
Refined asymptotic expansions for nonlocal diffusion equations |
| title_full |
Refined asymptotic expansions for nonlocal diffusion equations |
| title_fullStr |
Refined asymptotic expansions for nonlocal diffusion equations |
| title_full_unstemmed |
Refined asymptotic expansions for nonlocal diffusion equations |
| title_sort |
refined asymptotic expansions for nonlocal diffusion equations |
| url |
http://hdl.handle.net/20.500.12110/paper_14243199_v8_n4_p617_Ignat |
| work_keys_str_mv |
AT ignatli refinedasymptoticexpansionsfornonlocaldiffusionequations AT rossijd refinedasymptoticexpansionsfornonlocaldiffusionequations |
| _version_ |
1807315604659503104 |