scholarly journals A non-local problem for the Fokker-Planck equation related to the Becker-Döring model

2019 ◽  
Vol 39 (4) ◽  
pp. 1821-1889 ◽  
Author(s):  
Joseph G. Conlon ◽  
◽  
André Schlichting ◽  
Keyword(s):  
Planck Equation ◽  
Local Problem ◽  
Fokker Planck Equation ◽  
Non Local ◽  
Fokker Planck

scholarly journals A non-local scalar conservation law describing navigation processes

2020 ◽  
Vol 17 (04) ◽  
pp. 809-841
Author(s):  
Paulo Amorim ◽  
Florent Berthelin ◽  
Thierry Goudon
Keyword(s):  
Conservation Law ◽  
Stability Result ◽  
Planck Equation ◽  
Small Region ◽  
Effective Velocity ◽  
Fokker Planck Equation ◽  
Scalar Conservation Law ◽  
Non Local ◽  
Scalar Conservation ◽  
Fokker Planck

We consider a non-local scalar conservation law in two space dimensions which arises as the formal hydrodynamic limit of a Fokker–Planck equation. This Fokker–Planck equation is, in turn, the kinetic description of an individual-based model describing the navigation of self-propelled particles in a pheromone landscape. The pheromone may be linked to the agent distribution itself, leading to a nonlinear, non-local scalar conservation law where the effective velocity vector depends on the pheromone field in a small region around each point, and thus, on the solution itself. After presenting and motivating the problem, we present some numerical simulations of a closely related problem, and then prove a well-posedness and stability result for the conservation law.

AN APPLICATION OF FOKKER–PLANCK EQUATION TO JOSEPHSON JUNCTION

1989 ◽  
Vol 9 (1) ◽  
pp. 109-120
Author(s):  
G. Liao ◽  
A.F. Lawrence ◽  
A.T. Abawi
Keyword(s):  
Josephson Junction ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Fokker Planck

scholarly journals Time-changed fractional Ornstein-Uhlenbeck process

2020 ◽  
Vol 23 (2) ◽  
pp. 450-483 ◽  
Author(s):  
Giacomo Ascione ◽  
Yuliya Mishura ◽  
Enrica Pirozzi
Keyword(s):  
Planck Equation ◽  
Uhlenbeck Process ◽  
Fokker Planck Equation ◽  
Ornstein Uhlenbeck Process ◽  
Fokker Planck

AbstractWe define a time-changed fractional Ornstein-Uhlenbeck process by composing a fractional Ornstein-Uhlenbeck process with the inverse of a subordinator. Properties of the moments of such process are investigated and the existence of the density is shown. We also provide a generalized Fokker-Planck equation for the density of the process.

Sign in / Sign up

Export Citation Format

Share Document