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DOI: 10.23952/cot.2022.2
Received October 21, 2021; Accepted February 22, 2022; Published March 3, 2022
Abstract. In this paper, we discuss a situation, which could lead to both wave turbulence and collective behavior kinetic equations. The wave turbulence kinetic models appear in the kinetic limit when the wave equations have local differential operators. Viewing wave equations on the lattice as chains of anharmonic oscillators and replacing the local differential operators (short-range interactions) by non-local ones (long-range interactions), we arrive at a new Vlasov-type kinetic model in the mean field limit under the molecular chaos assumption reminiscent of models for collective behavior in which anharmonic oscillators replace individual particles.
How to Cite this Article:
A. Aceves, R. Alonso, M.-B. Tran, Wave turbulence and collective behavior models for wave equations with short- and long-range interactions, Commun. Optim. Theory 2022 (2022) 2.