Global Weak Solutions for Kolmogorov-vicsek Type Equations with Orientational Interaction
نویسنده
چکیده
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 with a velocity of constant magnitude. Therefore, the velocity variable of kinetic Kolmogorov-Vicsek models lies on the unit sphere. For our analysis, we take advantage of the boundedness of velocity space to get L estimates and compactness property.
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., ...
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