Stability analysis of a Vlasov-Wave system describing particles interacting with their environment

Abstract : We study a kinetic equation of the Vlasov-Wave type, which arises in the description of the behaviour of a large number of particles interacting weakly with an environment, composed of an infinite collection of local vibrational degrees of freedom, modeled by wave equations. We use variational techniques to establish the existence of large families of stationary states for this system, and analyze their stability.
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Stephan de Bièvre, Thierry Goudon, Arthur Vavasseur. Stability analysis of a Vlasov-Wave system describing particles interacting with their environment. Journal of Differential Equations, Elsevier, 2018, 264 (12), pp.7069-7093. ⟨hal-01581676⟩

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