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Improved energy methods for nonlocal diffusion problems
dc.contributor.author | Cañizo Rincón, José Alfredo | |
dc.contributor.author | Molino Salas, Alexis | |
dc.date.accessioned | 2019-06-24T01:22:01Z | |
dc.date.available | 2019-06-24T01:22:01Z | |
dc.date.issued | 2018 | |
dc.identifier.citation | José A. Cañizo, Alexis Molino. Improved energy methods for nonlocal diffusion problems. Discrete & Continuous Dynamical Systems - A, 2018, 38 (3) : 1405-1425. doi: 10.3934/dcds.2018057. | es_ES |
dc.identifier.issn | 1078-0947 | |
dc.identifier.issn | 1553-5231 | |
dc.identifier.uri | http://hdl.handle.net/10481/56086 | |
dc.description.abstract | We prove an energy inequality for nonlocal diffusion operators of the following type, and some of its generalisations: L u ( x ) := ∫ R N K ( x , y ) ( u ( y ) − u ( x ) ) d y , where L acts on a real function u defined on R N , and we assume that K ( x , y ) is uniformly strictly positive in a neighbourhood of x = y . The inequality is a nonlocal analogue of the Nash inequality, and plays a similar role in the study of the asymptotic decay of solutions to the nonlocal diffusion equation ∂ t u = L u as the Nash inequality does for the heat equation. The inequality allows us to give a precise decay rate of the L p norms of u and its derivatives. As compared to existing decay results in the literature, our proof is perhaps simpler and gives new results in some cases. | es_ES |
dc.description.sponsorship | J. A. Cañizo was supported by the Spanish Ministerio de Economía y Competitividad and the European Regional Development Fund (ERDF/FEDER), project MTM2014-52056-P. A. Molino was partially supported by MINECO - FEDER GrantMTM2015-68210-P(Spain), Junta de Andalucía FQM-116 (Spain) andMINECO Grant BES-2013-066595 (Spain). | es_ES |
dc.language.iso | eng | es_ES |
dc.publisher | American Institute of Mathematical Sciences (AIMS) | es_ES |
dc.rights | Atribución 3.0 España | * |
dc.rights.uri | http://creativecommons.org/licenses/by/3.0/es/ | * |
dc.subject | Nonlocal diffusion | es_ES |
dc.subject | Entropy methods | es_ES |
dc.subject | Energy methods | es_ES |
dc.subject | Asymptotic behaviour | es_ES |
dc.title | Improved energy methods for nonlocal diffusion problems | es_ES |
dc.type | journal article | es_ES |
dc.rights.accessRights | open access | es_ES |