Publication:
Homogenization in a thin domain with an oscillatory boundary

dc.contributor.authorArrieta Algarra, José María
dc.contributor.authorPereira, Marcone C.
dc.date.accessioned2023-06-20T00:06:28Z
dc.date.available2023-06-20T00:06:28Z
dc.date.issued2011
dc.description.abstractIn this paper we analyze the behavior of the Laplace operator with Neumann boundary conditions in a thin domain of the type where the function G(x,y) is periodic in y of period L. Observe that the upper boundary of the thin domain presents a highly oscillatory behavior and, moreover, the height of the thin domain, the amplitude and period of the oscillations are all of the same order, given by the small parameter ϵ.
dc.description.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.sponsorshipDGES
dc.description.sponsorshipPC
dc.description.sponsorshipMICINN
dc.description.sponsorshipBSCH-UCM, Spain
dc.description.sponsorshipFAPESP
dc.description.sponsorshipCAPES DGU
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/13402
dc.identifier.citation[1] Y. Amirat, O. Bodart, U. de Maio, A. Gaudiello, “Asymptotic Approximation of the solution of the Laplace equation in a domain with highly oscillating boundary", SIAM J. Math. Anal. 35, 1598-1616 (2004) [2] J. M. Arrieta, Spectral properties of Schrödinger operators under perturbations of the domain, Ph.D. Thesis, Georgia Institute of Technology, (1991) [3] J. M. Arrieta and M. C. Pereira, “Elliptic problems in thin domains with highly oscillating boundaries", Bol. Soc. Esp. Mat. Apl., to appear. [4] J. M. Arrieta, A. N. Carvalho, M. C. Pereira and R. P. da Silva; “Attractors in thin domains with a highly oscillatory boundary", Submitted. [5] A. Bensoussan, J. L. Lions and G. Papanicolaou, Asymptotic Analysis for Periodic Structures, North-Holland Publishing Company (1978). [6] R. Brizzi, J.P. Chalot, “Boundary homogenization and Neumann boundary problem" Ricerce di Matematica XLVI, 2 (1997) 341-387 [7] V. Burenkov, P.D. Lamberti, “Spectral Stability of general non-negarive self-adjoint operators with applications to Neumann-type operators", J. Differential Equations 233 (2007), 345-379 [8] D. Cioranescu and J. Saint Jean Paulin; Homogenization of Reticulated Structures, Springer Verlag (1980). [9] A. Damlamian, K. Pettersson, “Homogenization of oscillating boundaries" , Discrete and Continuous Dynamical Systems 23, (2009), 197-219 [10] J. K. Hale and G. Raugel, “Reaction-diffusion equation on thin domains", J. Math. Pures and Appl. (9) 71, no. 1, 33-95 (1992). [11] G. Raugel; Dynamics of partial differential equations on thin domains in Dynamical systems (Montecatini Terme, 1994), 208-315, Lecture Notes in Math., 1609, Springer, Berlin, 1995. [12] E. Sánchez-Palencia, Non-Homogeneous Media and Vibration Theory, Lecture Notes in Physics 127, Springer Verlag (1980) [13] L. Tartar; Problèmmes d'homogénéisation dans les équations aux dérivées partielles, Cours Peccot, Collège de France (1977). [14] L. Tartar, “Quelques remarques sur l'homegénéisation", Function Analysis and Numerical Analysis, Proc. Japan-France Seminar 1976, ed. H. Fujita, Japanese Society for the Promotion of Science, 468-482 (1978).
dc.identifier.doi10.1016/j.matpur.2011.02.003
dc.identifier.issn0021-7824
dc.identifier.officialurlhttp://www.sciencedirect.com/science/journal/00217824
dc.identifier.urihttps://hdl.handle.net/20.500.14352/41983
dc.issue.number1
dc.journal.titleJournal de Mathématiques Pures et Appliquées
dc.language.isoeng
dc.page.final57
dc.page.initial29
dc.publisherElsevier
dc.relation.projectIDMTM2009-07540
dc.relation.projectIDMTM2006-08262
dc.relation.projectIDPHB2006-003 PC
dc.relation.projectIDPR2009-0027
dc.relation.projectIDGR58/08
dc.relation.projectIDGrupo 920894 “Comportamiento Asintótico y Dinámica de Ecuaciones Diferenciales-CADEDIF”
dc.relation.projectID2008/53094-4
dc.relation.projectID127/07
dc.relation.projectID305210/2008-4
dc.rights.accessRightsopen access
dc.subject.cdu517.9
dc.subject.keywordThin domain
dc.subject.keywordOscillating boundary
dc.subject.keywordHomogenization
dc.subject.keywordExtension operator
dc.subject.ucmEcuaciones diferenciales
dc.subject.unesco1202.07 Ecuaciones en Diferencias
dc.titleHomogenization in a thin domain with an oscillatory boundary
dc.typejournal article
dc.volume.number96
dspace.entity.typePublication
relation.isAuthorOfPublication2f8ee04e-dfcb-4000-a2ae-18047c5f0f4a
relation.isAuthorOfPublication.latestForDiscovery2f8ee04e-dfcb-4000-a2ae-18047c5f0f4a
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