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

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

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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• http://mi.mathnet.ru/eng/smj1446
• http://mi.mathnet.ru/eng/smj/v42/i3/p585

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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. Akhmetov DR, Lavrentiev MM, Spigler R, “Singular perturbations for certain partial differential equations without boundary-layers”, Asymptotic Analysis, 35:1 (2003), 65–89
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
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
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
5. Akhmetov D.R., Lavrentiev M.M., Spigler R., “Singular perturbations of parabolic equations without boundary layers”, Appl Anal, 90:12 (2011), 1803–1818