On the structure of the singular set for the kinetic Fokker-Planck equations in domains with boundaries. Abstract: In this paper we compute asymptotics of solutions of the kinetic Fokker-Planck equation with inelastic boundary conditions which indicate that the solutions are nonunique if. The nonuniqueness is due to the fact that different solutions can interact in a different manner with a Dirac mass which appears at the singular point. In particular, this nonuniqueness explains the different behaviours found in the physics literature for numerical simulations of the stochastic differential equation associated to the kinetic Fokker-Planck equation. The asymptotics obtained in this paper will be used in a companion paper Nonuniqueness for the kinetic-Fokker-Planck equation with inelastic boundary conditions to prove rigorously nonuniqueness of solutions for the kinetic Fokker-Planck equation with inelastic boundary conditions. References [Enhancements On Off] What's this?
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We'd like to understand how you use our websites in order to improve them. Register your interest. We study the initial-boundary value problem for the Fokker—Planck equation in an interval with absorbing boundary conditions.
We develop a theory of well-posedness of classical solutions for the problem. We also prove that the resulting solutions decay exponentially for long times.
This is a preview of subscription content, log in to check access. Rent this article via DeepDyve. Abramovich M. Dover, New York Google Scholar. Bouchut F. Pures Appl. Bonilla L. SIAM J. Burkhardt T. A Math. Carrillo J. Methods Appl. Carpio A. Desvillettes, L. Pure Appl. Evans L. AMS, Providence Friedman A. Dover Publications, New York Guo Y.
Gilbarg D. Springer, New York Hwang H. Discrete Contin. B 18 3 , — Acta Math. Hagan P. Herau F. Theory Probab. Ladyshenskaya, O. Nauka, Moscow, in Russian. Marshall T. It comes to earth, I know not when. Masoliver J. McKean H. Kyoto Univ. Mischler S. Super 4 43 5 , — Ono K. Systems 6 4 , — Protter M. Springer, Berlin Rein G. Sinai, Y. Stein E. Princeton University Press, Princeton Tikhonov A. Victory H. Indiana Univ.
Villani, C. Download references. Correspondence to Hyung Ju Hwang. Reprints and Permissions. Hwang, H. Arch Rational Mech Anal , — Download citation. Received : 06 November Accepted : 11 April Published : 22 May Issue Date : October Search SpringerLink Search. Abstract We study the initial-boundary value problem for the Fokker—Planck equation in an interval with absorbing boundary conditions.
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NIST Digital Library of Mathematical Functions
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The Fokker–Planck Equation with Absorbing Boundary Conditions
We'd like to understand how you use our websites in order to improve them. Register your interest. We study the initial-boundary value problem for the Fokker—Planck equation in an interval with absorbing boundary conditions. We develop a theory of well-posedness of classical solutions for the problem.