Decay estimates for nonlocal problems via energy methods
In this paper we study the applicability of energy methods to obtain bounds for the asymptotic decay of solutions to nonlocal diffusion problems. With these energy methods we can deal with nonlocal problems that not necessarily involve a convolution, that is, of the form ut (x, t) = ∫Rd G (x - y) (u...
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2009
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00217824_v92_n2_p163_Ignat https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00217824_v92_n2_p163_Ignat_oai |
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I28-R145-paper_00217824_v92_n2_p163_Ignat_oai2024-08-16 Ignat, L.I. Rossi, J.D. 2009 In this paper we study the applicability of energy methods to obtain bounds for the asymptotic decay of solutions to nonlocal diffusion problems. With these energy methods we can deal with nonlocal problems that not necessarily involve a convolution, that is, of the form ut (x, t) = ∫Rd G (x - y) (u (y, t) - u (x, t)) d y. For example, we will consider equations like,ut (x, t) = under(∫, Rd) J (x, y) (u (y, t) - u (x, t)) d y + f (u) (x, t), and a nonlocal analogous to the p-Laplacian,ut (x, t) = under(∫, Rd) J (x, y) | u (y, t) - u (x, t) |p - 2 (u (y, t) - u (x, t)) d y . The energy method developed here allows us to obtain decay rates of the form,{norm of matrix} u (ṡ, t) {norm of matrix}Lq (Rd) ≤ C t- α, for some explicit exponent α that depends on the parameters, d, q and p, according to the problem under consideration. © 2009 Elsevier Masson SAS. All rights reserved. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. application/pdf http://hdl.handle.net/20.500.12110/paper_00217824_v92_n2_p163_Ignat info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar J. Math. Pures Appl. 2009;92(2):163-187 Energy methods Nonlocal diffusion p-Laplacian Decay estimates for nonlocal problems via energy methods info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00217824_v92_n2_p163_Ignat_oai |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-145 |
| collection |
Repositorio Digital de la Universidad de Buenos Aires (UBA) |
| topic |
Energy methods Nonlocal diffusion p-Laplacian |
| spellingShingle |
Energy methods Nonlocal diffusion p-Laplacian Ignat, L.I. Rossi, J.D. Decay estimates for nonlocal problems via energy methods |
| topic_facet |
Energy methods Nonlocal diffusion p-Laplacian |
| description |
In this paper we study the applicability of energy methods to obtain bounds for the asymptotic decay of solutions to nonlocal diffusion problems. With these energy methods we can deal with nonlocal problems that not necessarily involve a convolution, that is, of the form ut (x, t) = ∫Rd G (x - y) (u (y, t) - u (x, t)) d y. For example, we will consider equations like,ut (x, t) = under(∫, Rd) J (x, y) (u (y, t) - u (x, t)) d y + f (u) (x, t), and a nonlocal analogous to the p-Laplacian,ut (x, t) = under(∫, Rd) J (x, y) | u (y, t) - u (x, t) |p - 2 (u (y, t) - u (x, t)) d y . The energy method developed here allows us to obtain decay rates of the form,{norm of matrix} u (ṡ, t) {norm of matrix}Lq (Rd) ≤ C t- α, for some explicit exponent α that depends on the parameters, d, q and p, according to the problem under consideration. © 2009 Elsevier Masson SAS. All rights reserved. |
| format |
Artículo Artículo publishedVersion |
| author |
Ignat, L.I. Rossi, J.D. |
| author_facet |
Ignat, L.I. Rossi, J.D. |
| author_sort |
Ignat, L.I. |
| title |
Decay estimates for nonlocal problems via energy methods |
| title_short |
Decay estimates for nonlocal problems via energy methods |
| title_full |
Decay estimates for nonlocal problems via energy methods |
| title_fullStr |
Decay estimates for nonlocal problems via energy methods |
| title_full_unstemmed |
Decay estimates for nonlocal problems via energy methods |
| title_sort |
decay estimates for nonlocal problems via energy methods |
| publishDate |
2009 |
| url |
http://hdl.handle.net/20.500.12110/paper_00217824_v92_n2_p163_Ignat https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00217824_v92_n2_p163_Ignat_oai |
| work_keys_str_mv |
AT ignatli decayestimatesfornonlocalproblemsviaenergymethods AT rossijd decayestimatesfornonlocalproblemsviaenergymethods |
| _version_ |
1809357194670374912 |