dc.creator | Pérez Llanos, Mayte | es |
dc.creator | Rossi, Julio D. | es |
dc.date.accessioned | 2023-01-31T11:54:59Z | |
dc.date.available | 2023-01-31T11:54:59Z | |
dc.date.issued | 2011-01-01 | |
dc.identifier.citation | Pérez Llanos, M. y Rossi, J.D. (2011). Numerical approximations for a nonlocal evolution equation. SIAM Journal on numerical analysis, 49 (5/6), 2103-2123. https://doi.org/10.1137/110823559. | |
dc.identifier.issn | 0036-1429 | es |
dc.identifier.issn | 1095-7170 | es |
dc.identifier.uri | https://hdl.handle.net/11441/142224 | |
dc.description.abstract | In this paper we study numerical approximations of continuous solutions to the
nonlocal p-Laplacian type diffusion equation, ut(t, x) =
Ω J(x − y)|u(t, y) − u(t, x)|
p−2(u(t, y) −
u(t, x)) dy. First, we find that a semidiscretization in space of this problem gives rise to an ODE
system whose solutions converge uniformly to the continuous one as the mesh size goes to zero.
Moreover, the semidiscrete approximation shares some properties of the continuous problem: it
preserves the total mass and the solution converges to the mean value of the initial condition as t
goes to infinity. Next, we also discretize the time variable and present a totally discrete method
which also enjoys the above mentioned properties. In addition, we investigate the limit as p goes to
infinity in these approximations and obtain a discrete model for the evolution of a sandpile. Finally,
we present some numerical experiments that illustrate our results. | es |
dc.format | application/pdf | es |
dc.format.extent | 22 p. | es |
dc.language.iso | eng | es |
dc.publisher | SIAM | es |
dc.relation.ispartof | SIAM Journal on numerical analysis, 49 (5/6), 2103-2123. | |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.subject | numerical approximations | es |
dc.subject | nonlocal diffusion | es |
dc.subject | p-Laplacian | es |
dc.subject | Neumann boundary conditions | es |
dc.subject | sandpiles | es |
dc.title | Numerical approximations for a nonlocal evolution equation | es |
dc.type | info:eu-repo/semantics/article | es |
dcterms.identifier | https://ror.org/03yxnpp24 | |
dc.type.version | info:eu-repo/semantics/publishedVersion | es |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es |
dc.contributor.affiliation | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico | es |
dc.relation.publisherversion | https://doi.org/10.1137/110823559 | es |
dc.identifier.doi | 10.1137/110823559 | es |
dc.contributor.group | Universidad de Sevilla. FQM131: Ec.diferenciales,Simulacion Num.y Desarrollo Software | es |
dc.journaltitle | SIAM Journal on numerical analysis | es |
dc.publication.volumen | 49 | es |
dc.publication.issue | 5/6 | es |
dc.publication.initialPage | 2103 | es |
dc.publication.endPage | 2123 | es |