For localized initial data, solutions to the Vlasov-Poisson system in C^3 convex domains with conducting walls have velocities asymptotically supported in the closure of a new asymptotic domain D_∞ and exhibit modified scattering.
Bigorgne, Global existence and modified scattering for the small data solutions to the Vlasov-Maxwell system
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The Vlasov-Poisson system with a perfectly conducting wall: Convex domains
For localized initial data, solutions to the Vlasov-Poisson system in C^3 convex domains with conducting walls have velocities asymptotically supported in the closure of a new asymptotic domain D_∞ and exhibit modified scattering.