Fokker-Planck equation in bounded domain. (English) Zbl 1200.35305
This paper is concerned with the existence and uniqueness of a solution to the well-studied linear Fokker-Planck equation in a bounded domain. The author nicely presents tools from differential geometry as well as lemmas used in the main proof of the theorem. He then gives the precise statement of the main part before providing the proof of the theorem which consists of two parts, the existence and the uniquneness. The last part of the paper provides an application to fluid mechanics with numerical results. The article is well-referenced and is a welcome addition to the literature on these type of linear equations which occur in many application in physics and finance.
Reviewer: F. M. Mahomed (Johannesburg)
MSC:
| 35Q84 | Fokker-Planck equations |
| 35Q35 | PDEs in connection with fluid mechanics |
| 35J25 | Boundary value problems for second-order elliptic equations |
| 35R60 | PDEs with randomness, stochastic partial differential equations |
| 76A05 | Non-Newtonian fluids |
| 82D60 | Statistical mechanics of polymers |
Keywords:
Fokker-Planck equation; bounded domain; stationary solution; confinement; fluid mechanics; polymer flowsReferences:
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