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Sibirsk. Mat. Zh., 2001, Volume 42, Number 3, Pages 585–609 (Mi smj1446)  

This article is cited in 5 scientific papers (total in 5 papers)

Nonlinear integroparabolic equations on unbounded domains: existence of classical solutions with special properties

M. M. Lavrent'ev (Jn.)a, R. Spiglerb, D. R. Akhmetova

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Università degli Studi Roma Tre, Dipartimento di Matematica Largo San Leonardo Murialdo, 1, 00146 Roma (Italia)

Abstract: Classical solvability is established for a certain nonlinear integrodifferential parabolic equation, on unbounded domains in several dimensions. The model equation of the Fokker–Planck type represents a regularized version of an equation recently derived by J. A. Acebron and R. Spigler for the physical problem of describing the time evolution of large populations of nonlinearly globally coupled random oscillators. Precise estimates are obtained for the decay of convolutions with fundamental solutions of linear parabolic equations on unbounded domains in $R^n$. Existence of a classical solution with special properties is established.

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English version:
Siberian Mathematical Journal, 2001, 42:3, 495–516

Bibliographic databases:

UDC: 517.95
Received: 18.10.2000

Citation: M. M. Lavrent'ev (Jn.), R. Spigler, D. R. Akhmetov, “Nonlinear integroparabolic equations on unbounded domains: existence of classical solutions with special properties”, Sibirsk. Mat. Zh., 42:3 (2001), 585–609; Siberian Math. J., 42:3 (2001), 495–516

Citation in format AMSBIB
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\pages 585--609
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\transl
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\crossref{https://doi.org/10.1023/A:1010423209940}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Akhmetov DR, Lavrentiev MM, Spigler R, “Singular perturbations for certain partial differential equations without boundary-layers”, Asymptotic Analysis, 35:1 (2003), 65–89  mathscinet  zmath  isi
    2. Lavrentiev Jr. Mikhail M., “Time-Independent Estimates and a Comparison Theorem for a Nonlinear Integroparabolic Equation of the Fokker-Planck Type”, Differ. Integral Equ., 17:5-6 (2004), 549–570  mathscinet  zmath  isi
    3. Akhmetov D.R. Lavrentiev Jr. Mikhail M. Spigler R., “Singular Perturbations for Parabolic Equations with Unbounded Coefficients Leading to Ultraparabolic Equations”, Differ. Integral Equ., 17:1-2 (2004), 99–118  mathscinet  zmath  isi
    4. Akhmetov D.R., Spigler R., “Uniform and optimal estimates for solutions to singularly perturbed parabolic equations”, Journal of Evolution Equations, 7:2 (2007), 347–372  crossref  mathscinet  zmath  isi  scopus
    5. Akhmetov D.R., Lavrentiev M.M., Spigler R., “Singular perturbations of parabolic equations without boundary layers”, Appl Anal, 90:12 (2011), 1803–1818  crossref  mathscinet  zmath  isi  elib  scopus
  • Сибирский математический журнал Siberian Mathematical Journal
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