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    Nonlocal higher order evolution equations

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    Type
    Article
    Authors
    Rossi, Julio D.
    Schönlieb, Carola-Bibiane
    KAUST Grant Number
    KUK-I1-007-43
    Date
    2010-06
    Permanent link to this record
    http://hdl.handle.net/10754/598997
    
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    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.
    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).
    Publisher
    Informa UK Limited
    Journal
    Applicable Analysis
    DOI
    10.1080/00036811003735824
    ae974a485f413a2113503eed53cd6c53
    10.1080/00036811003735824
    Scopus Count
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    Publications Acknowledging KAUST Support

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