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dc.contributor.authorAkhmetov, Denis R. ( )
dc.contributor.authorLavrentiev, Mikhail M. ( )
dc.contributor.authorSpigler, Renato ( Orcid Icon 0000-0002-4561-4845 )
dc.date.accessioned2020-07-15T17:23:22Z
dc.date.available2020-07-15T17:23:22Z
dc.date.issued2002-02-27
dc.identifier.citationAkhmetov, D. R., Lavrentiev, M. M., & Spigler, R. (2002). Existence and uniqueness of classical solutions to certain nonlinear integro-differential Fokker-Planck type equations. Electronic Journal of Differential Equations, 2002(24), pp. 1-17.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/12088
dc.description.abstractA nonlinear Fokker-Planck type ultraparabolic integro-differential equation is studied. It arises from the statistical description of the dynamical behavior of populations of infinitely many (nonlinearly coupled) random oscillators subject to ``mean-field'' interaction. A regularized parabolic equation with bounded coefficients is first considered, where a small spatial diffusion is incorporated in the model equation and the unbounded coefficients of the original equation are replaced by a special ``bounding" function. Estimates, uniform in the regularization parameters, allow passing to the limit, which identifies a classical solution to the original problem. Existence and uniqueness of classical solutions are then established in a special class of functions decaying in the velocity variable.en_US
dc.formatText
dc.format.extent17 pages
dc.format.medium1 file (.pdf)
dc.language.isoen_USen_US
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2002, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectNonlinear integro-differential parabolic equationsen_US
dc.subjectUltraparabolic equationsen_US
dc.subjectFokker-Planck equationen_US
dc.subjectDegenerate parabolic equationsen_US
dc.subjectRegularizationen_US
dc.titleExistence and Uniqueness of Classical Solutions to Certain Nonlinear Integro-Differential Fokker-Planck Type Equationsen_US
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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