Existence and Uniqueness of Classical Solutions to Certain Nonlinear Integro-Differential Fokker-Planck Type Equations
dc.contributor.author | Akhmetov, Denis R. ( ) | |
dc.contributor.author | Lavrentiev, Mikhail M. ( ) | |
dc.contributor.author | Spigler, Renato ( ![]() | |
dc.date.accessioned | 2020-07-15T17:23:22Z | |
dc.date.available | 2020-07-15T17:23:22Z | |
dc.date.issued | 2002-02-27 | |
dc.identifier.citation | Akhmetov, 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.issn | 1072-6691 | |
dc.identifier.uri | https://digital.library.txstate.edu/handle/10877/12088 | |
dc.description.abstract | A 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.format | Text | |
dc.format.extent | 17 pages | |
dc.format.medium | 1 file (.pdf) | |
dc.language.iso | en | en_US |
dc.publisher | Southwest Texas State University, Department of Mathematics | en_US |
dc.source | Electronic Journal of Differential Equations, 2002, San Marcos, Texas: Southwest Texas State University and University of North Texas. | |
dc.subject | Nonlinear integro-differential parabolic equations | en_US |
dc.subject | Ultraparabolic equations | en_US |
dc.subject | Fokker-Planck equation | en_US |
dc.subject | Degenerate parabolic equations | en_US |
dc.subject | Regularization | en_US |
dc.title | Existence and Uniqueness of Classical Solutions to Certain Nonlinear Integro-Differential Fokker-Planck Type Equations | en_US |
dc.type | publishedVersion | |
txstate.documenttype | Article | |
dc.rights.license | ![]() This work is licensed under a Creative Commons Attribution 4.0 International License. | |
dc.description.department | Mathematics |