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Mathematics > Analysis of PDEs
Title: Derivation of a Boltzmann equation with higher-order collisions from a generalized Kac model
(Submitted on 4 Nov 2022 (v1), last revised 8 Nov 2022 (this version, v2))
Abstract: In this work, we generalize M. Kac's original many-particle binary stochastic model to derive a space homogeneous Boltzmann equation that includes a linear combination of higher-order collisional terms. First, we prove an abstract theorem about convergence from a finite hierarchy to an infinite hierarchy of coupled equations. We apply this convergence theorem on hierarchies for marginals corresponding to the generalized Kac model mentioned above. As a corollary, we prove propagation of chaos for the marginals associated to the generalized Kac model. In particular, the first marginal converges towards the solution of a Boltzmann equation including interactions up to a finite order, and whose collision kernel is of Maxwell-type with cut-off.
Submission history
From: William Warner [view email][v1] Fri, 4 Nov 2022 21:47:51 GMT (45kb)
[v2] Tue, 8 Nov 2022 06:35:03 GMT (45kb)
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