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초록
We consider the so-called spatially homogenous Kolmogorov-Vicsek model, a non-linear Fokker-Planck equation of self-driven stochastic particles with orientation interaction under the space-homogeneity. We prove the global existence and uniqueness of weak solutions to the equation. We also show that weak solutions exponentially converge to a steady state, which has the form of the Fisher-von Mises distribution.
키워드
SELF-DRIVEN PARTICLES; ORIENTATION INTERACTION; PHASE-TRANSITIONS; DYNAMICS; LIMIT; MANIFOLDS; EQUATIONS
- 제목
- Global Well-posedness of the Spatially Homogeneous Kolmogorov-Vicsek Model as a Gradient Flow
- 저자
- Figalli, Alessio; Kang, Moon-Jin; Morales, Javier
- 발행일
- 2018-03
- 유형
- Article
- 권
- 227
- 호
- 3
- 페이지
- 869 ~ 896