Handle URI:
http://hdl.handle.net/10754/598997
Title:
Nonlocal higher order evolution equations
Authors:
Rossi, Julio D.; Schönlieb, Carola-Bibiane
Abstract:
In this article, we study the asymptotic behaviour of solutions to the nonlocal operator ut(x, t)1/4(-1)n-1 (J*Id -1)n (u(x, t)), x ∈ ℝN, which is the nonlocal analogous to the higher order local evolution equation vt(-1)n-1(Δ)nv. We prove that the solutions of the nonlocal problem converge to the solution of the higher order problem with the right-hand side given by powers of the Laplacian when the kernel J is rescaled in an appropriate way. Moreover, we prove that solutions to both equations have the same asymptotic decay rate as t goes to infinity. © 2010 Taylor & Francis.
Citation:
Rossi JD, Schönlieb C-B (2010) Nonlocal higher order evolution equations. Applicable Analysis 89: 949–960. Available: http://dx.doi.org/10.1080/00036811003735824.
Publisher:
Informa UK Limited
Journal:
Applicable Analysis
KAUST Grant Number:
KUK-I1-007-43
Issue Date:
Jun-2010
DOI:
10.1080/00036811003735824
Type:
Article
ISSN:
0003-6811; 1563-504X
Sponsors:
C.-B. Schonlieb is partially supported by the DFG Graduiertenkolleg 1023 Identification in Mathematical Models: Synergy of Stochastic and Numerical Methods, by the project WWTF Five senses-Call 2006, Mathematical Methods for Image Analysis and Processing in the Visual Arts project No. CI06 003 and by the FFG project Erarbeitung neuer Algorithmen zum Image Inpainting project No. 813610. Further, this publication is based on the work supported by Award No. KUK-I1-007-43, made by King Abdullah University of Science and Technology (KAUST). J.D. Rossi is partially supported by UBA X066, CONICET (Argentina) and SIMUMAT (Spain).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorRossi, Julio D.en
dc.contributor.authorSchönlieb, Carola-Bibianeen
dc.date.accessioned2016-02-25T13:50:51Zen
dc.date.available2016-02-25T13:50:51Zen
dc.date.issued2010-06en
dc.identifier.citationRossi JD, Schönlieb C-B (2010) Nonlocal higher order evolution equations. Applicable Analysis 89: 949–960. Available: http://dx.doi.org/10.1080/00036811003735824.en
dc.identifier.issn0003-6811en
dc.identifier.issn1563-504Xen
dc.identifier.doi10.1080/00036811003735824en
dc.identifier.urihttp://hdl.handle.net/10754/598997en
dc.description.abstractIn this article, we study the asymptotic behaviour of solutions to the nonlocal operator ut(x, t)1/4(-1)n-1 (J*Id -1)n (u(x, t)), x ∈ ℝN, which is the nonlocal analogous to the higher order local evolution equation vt(-1)n-1(Δ)nv. We prove that the solutions of the nonlocal problem converge to the solution of the higher order problem with the right-hand side given by powers of the Laplacian when the kernel J is rescaled in an appropriate way. Moreover, we prove that solutions to both equations have the same asymptotic decay rate as t goes to infinity. © 2010 Taylor & Francis.en
dc.description.sponsorshipC.-B. Schonlieb is partially supported by the DFG Graduiertenkolleg 1023 Identification in Mathematical Models: Synergy of Stochastic and Numerical Methods, by the project WWTF Five senses-Call 2006, Mathematical Methods for Image Analysis and Processing in the Visual Arts project No. CI06 003 and by the FFG project Erarbeitung neuer Algorithmen zum Image Inpainting project No. 813610. Further, this publication is based on the work supported by Award No. KUK-I1-007-43, made by King Abdullah University of Science and Technology (KAUST). J.D. Rossi is partially supported by UBA X066, CONICET (Argentina) and SIMUMAT (Spain).en
dc.publisherInforma UK Limiteden
dc.subjectAsymptotic behaviouren
dc.subjectHigher orderen
dc.subjectNonlocal diffusionen
dc.titleNonlocal higher order evolution equationsen
dc.typeArticleen
dc.identifier.journalApplicable Analysisen
dc.contributor.institutionUniversidad de Buenos Aires, Buenos Aires, Argentinaen
dc.contributor.institutionUniversitat Gottingen, Gottingen, Germanyen
kaust.grant.numberKUK-I1-007-43en
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