Existence and Uniqueness of Classical Solutions to Certain Nonlinear Integro-Differential Fokker-Planck Type Equations

Simple item page
dc.contributor.authorAkhmetov, Denis R.
dc.contributor.authorLavrentiev, Mikhail M.
dc.contributor.authorSpigler, Renato
dc.date.accessioned2020-07-15T17:23:22Z
dc.date.available2020-07-15T17:23:22Z
dc.date.issued2002-02-27
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.
dc.description.departmentMathematics
dc.formatText
dc.format.extent17 pages
dc.format.medium1 file (.pdf)
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. <i>Electronic Journal of Differential Equations, 2002</i>(24), pp. 1-17.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/12088
dc.language.isoen
dc.publisherSouthwest Texas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2002, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectNonlinear integro-differential parabolic equations
dc.subjectUltraparabolic equations
dc.subjectFokker-Planck equation
dc.subjectDegenerate parabolic equations
dc.subjectRegularization
dc.titleExistence and Uniqueness of Classical Solutions to Certain Nonlinear Integro-Differential Fokker-Planck Type Equations
dc.typeArticle

Files

Original bundle

Now showing 1 - 1 of 1
Thumbnail Image
Name:
akhmetov.pdf
Size:
272.73 KB
Format:
Adobe Portable Document Format
Description:
Download

License bundle

Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
2.54 KB
Format:
Item-specific license agreed upon to submission
Description:
Download

Collections

Electronic Journal of Differential Equations