Towards optimal regularity for the fourth-order thin film equation in RN: Graveleau-type focusing self-similarity

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dc.contributor.author Álvarez Caudevilla, Pablo
dc.contributor.author Evans, J. D.
dc.contributor.author Galaktionov, Victor A.
dc.date.accessioned 2021-03-24T11:12:36Z
dc.date.available 2021-03-24T11:12:36Z
dc.date.issued 2015-11-15
dc.identifier.bibliographicCitation Álvarez-Caudevilla, P., Evans, J. D. & Galaktionov, V. A. (2015). Towards optimal regularity for the fourth-order thin film equation in RN: Graveleau-type focusing self-similarity. Journal of Mathematical Analysis and Applications, 431(2), pp. 1099–1123.
dc.identifier.issn 0022-247X
dc.identifier.uri http://hdl.handle.net/10016/32213
dc.description.abstract An approach to some "optimal" (more precisely, non-improvable) regularity of solutions of the thin film equation ut = -del.(vertical bar u vertical bar(n)del Delta u) in R-N x R+, u(x,0) = u(0)(x) in R-N, where n is an element of (0,2) is a fixed exponent, with smooth compactly supported initial data u(0)(x), in dimensions N >= 2 is discussed. Namely, a precise exponent for the Hoder continuity with respect to the spatial radial variable vertical bar x vertical bar is obtained by construction of a Graveleau-type focusing self-similar solution. As a consequence, optimal regularity of the gradient del u in certain L-P spaces, as well as a Holder continuity property of solutions with respect to x and t, are derived, which cannot be obtained by classic standard methods of integral identities inequalities. Several profiles for the solutions in the cases n = 0 and n > 0 are also plotted. In general, we claim that, even for arbitrarily small n > 0 and positive analytic initial data u(0)(x), the solutions u(x,t) cannot be better than C-x(2-epsilon)-smooth, where epsilon(n) = O(n) as n -> 0.
dc.format.extent 25
dc.language.iso eng
dc.publisher Elsevier
dc.rights © 2015 Elsevier Inc.
dc.rights Atribución-NoComercial-SinDerivadas 3.0 España
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject.other Thin film equation in Rn
dc.subject.other Optimal regularity
dc.subject.other Graveleau-type focusing similarity
dc.subject.other Solutions
dc.subject.other Numerics
dc.title Towards optimal regularity for the fourth-order thin film equation in RN: Graveleau-type focusing self-similarity
dc.type article
dc.subject.eciencia Matemáticas
dc.identifier.doi https://doi.org/10.1016/j.jmaa.2015.06.027
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. MTM2012-33258
dc.type.version acceptedVersion
dc.identifier.publicationfirstpage 1099
dc.identifier.publicationissue 2
dc.identifier.publicationlastpage 1123
dc.identifier.publicationtitle Journal of Mathematical Analysis and Applications
dc.identifier.publicationvolume 431
dc.identifier.uxxi AR/0000017145
dc.contributor.funder Ministerio de Economía y Competitividad (España)
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