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Mat. Zametki, 2014, Volume 96, Issue 4, Pages 578–587 (Mi mz10405)  

This article is cited in 3 scientific papers (total in 3 papers)

A Parabolic Equation with Nonlocal Diffusion without a Smooth Inertial Manifold

A. V. Romanov

Moscow State Institute of Electronics and Mathematics — Higher School of Economics

Abstract: A family of parabolic integro-differential equations with nonlocal diffusion on the circle which have no smooth inertial manifold is presented.

Keywords: inertial manifold, semilinear parabolic equation, nonlocal diffusion, Hilbert integral operator.

DOI: https://doi.org/10.4213/mzm10405

Full text: PDF file (478 kB)
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English version:
Mathematical Notes, 2014, 96:4, 548–555

Bibliographic databases:

UDC: 517.95
Received: 14.08.2013
Revised: 15.02.2014

Citation: A. V. Romanov, “A Parabolic Equation with Nonlocal Diffusion without a Smooth Inertial Manifold”, Mat. Zametki, 96:4 (2014), 578–587; Math. Notes, 96:4 (2014), 548–555

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. V. Romanov, “On the hyperbolicity properties of inertial manifolds of reaction–diffusion equations”, Dyn. Partial Differ. Equ., 13:3 (2016), 263–272  crossref  mathscinet  zmath  isi  elib  scopus
    2. A. Kostianko, S. Zelik, “Inertial manifolds for 1D reaction-diffusion-advection systems. Part I: Dirichlet and Neumann boundary conditions”, Commun. Pure Appl. Anal, 16:6 (2017), 2357–2376  crossref  mathscinet  zmath  isi  scopus
    3. A. Kostianko, S. Zelik, “Inertial manifolds for 1D reaction-diffusion-advection systems. Part II: periodic boundary conditions”, Commun. Pure Appl. Anal, 17:1 (2018), 285–317  crossref  mathscinet  zmath  isi  scopus
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