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On the Cucker-Smale- Fokker-Planck Model under Random Environment
확률 환경 하에서의 쿠커-스메일-포커-플랑크 모델에 대하여

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Authors
정지인
Advisor
하승열
Major
자연과학대학 수리과학부
Issue Date
2016-08
Publisher
서울대학교 대학원
Keywords
flocking
Description
학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2016. 8. 하승열.
Abstract
In this dissertation, we mainly focus on a kinetic Cucker--Smale--Fokker--Planck (CS-FP) type equation with a degenerate diffusion coefficient. The CS-FP equation is described in a differential equation for a probability distribution function $f$ of the infinitely many Cucker--Smale flocking particles in a random environment. We will present a priori estimates for proving the global existence of classical solutions to the CS-FP equation. The global existence of classical solutions under a given sufficiently smooth initial datum will be obtained by applying sobolev embedding theorem to the a priori estimates and iterating the solutions of uniformly parabolic equations which approximates the CS-FP equation.
We also present the Cucker-Smale-Kuramoto model which describes flocking and synchronization coupled phenomena. Sufficient conditions for the asymptotic flocking and synchronization will be derived with the Lyapunov functional approach. We provide the numerical compuations for a special case to suggest the future works on clustering.
Language
Korean
URI
https://hdl.handle.net/10371/121319
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College of Natural Sciences (자연과학대학)Dept. of Mathematical Sciences (수리과학부)Theses (Ph.D. / Sc.D._수리과학부)
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