Titlebook: Recent Advances in Kinetic Equations and Applications; Francesco Salvarani Conference proceedings 2021 The Editor(s) (if applicable) and T

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The Vlasov Equation with Infinite Mass, the physical space and on the singularity of the interaction. In particular, for . = 3, the more singular the interaction, the faster must be the spatial decay at infinity of the initial distribution. We describe also an application which gives rise to a viscous friction model.

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The Half-Space Problem for the Boltzmann Equation with Phase Transition at the Boundary,r studies the existence and uniqueness of a uniformly, exponentially decaying solution in the vicinity of the Maxwellian equilibrium with zero bulk velocity, with the same temperature as that of the condensed phase, and whose pressure is the saturating vapor pressure at the temperature of the interf

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Recent Developments on Quasineutral Limits for Vlasov-Type Equations,s, unmagnetised plasma. In these notes, we discuss recent progress on the quasineutral limit in which the Debye length of the plasma tends to zero, an approximation widely assumed in applications. The models formally obtained from Vlasov-Poisson systems in this limit can be seen as kinetic formulati

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Control of Collective Dynamics with Time-Varying Weights,type, in which the objective is to drive all agents to a final target point under suitable control constraints. Controllability is discussed for the corresponding problem with and without constraints on the total mass of the system, and control strategies are designed with the steepest descent appro

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Kinetic Modelling of Autoimmune Diseases,y approach is used in order to describe the microscopic interactions between cells. Three cell populations are considered and the distribution function of each population depends on the biological activity variable defining the functional state relevant for that population. We revisit the wellposedn

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On the Accuracy of Gyrokinetic Equations in Fusion Applications, on the role of the electron–ion mass ratio in the gyrokinetic coordinate transformation. We discuss the ordering assumptions for the ITER and ASDEX Upgrade Tokamaks in detail. A system of generating differential equations is derived and solved by asymptotic expansion to second order for ions and to

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