Global Weak Solutions for Kolmogorov–Vicsek Type Equations with Orientational Interactions
نویسندگان
چکیده
منابع مشابه
Global Weak Solutions for Kolmogorov–Vicsek Type Equations with Orientational Interactions
We study the global existence and uniqueness of weak solutions to kinetic Kolmogorov–Vicsekmodels that canbe considered as non-local, non-linear, Fokker– Planck type equations describing the dynamics of individuals with orientational interactions. This model is derived from the discrete Couzin–Vicsek algorithm as mean-field limit (Bolley et al., Appl Math Lett, 25:339–343, 2012; Degond et al., ...
متن کاملGlobal Weak Solutions for Kolmogorov-vicsek Type Equations with Orientational Interaction
We study the global existence and uniqueness of weak solutions to kinetic Kolmogorov-Vicsek models that can be considered a non-local non-linear Fokker-Planck type equation describing the dynamics of individuals with orientational interaction. This model is derived from the discrete Couzin-Vicsek algorithm as mean-field limit [2, 9], which governs the interactions of stochastic agents moving wi...
متن کاملWeak Solutions for Dislocation Type Equations
We describe recent results obtained by G. Barles, P. Cardaliaguet, R. Monneau and the author in [9, 7]. They are concerned with nonlocal Eikonal equations arising in the study of the dynamics of dislocation lines in crystals. These equations are nonlocal but also non monotone. We use a notion of weak solution to provide solutions for all time. Then, we discuss the link between these weak soluti...
متن کاملExistence and uniqueness of weak solutions for a class of nonlinear divergence type diffusion equations
In this paper, we study the Neumann boundary value problem of a class of nonlinear divergence type diffusion equations. By a priori estimates, difference and variation techniques, we establish the existence and uniqueness of weak solutions of this problem.
متن کاملLandau-Lifshitz-Slonczewski Equations: Global Weak and Classical Solutions
We consider magnetization dynamics under the influence of a spin-polarized current, given in terms of a spin-velocity field v, governed by the following modification of the Landau– Lifshitz–Gilbert equation ∂m ∂t + v · ∇m = m × (α ∂m ∂t + β v · ∇m − Δm), called the Landau– Lifshitz–Slonczewski equation. We focus on the situation of magnetizations defined on the entire Euclidean space m(t) : R3 ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Archive for Rational Mechanics and Analysis
سال: 2016
ISSN: 0003-9527,1432-0673
DOI: 10.1007/s00205-016-1002-2