1,720,991 research outputs found
The Extended Phase Space Method in Kinetic Theory
No full textThis article describes the extended phase space technique in the study of kinetic equations and provides a review of some relevant contributions appeared in the literature
From the Boltzmann Description for Mixtures to the Maxwell–Stefan Diffusion Equations
No full textThis article reviews some recent results on the diffusion limit of the Boltzmann system for gaseous mixtures to the Maxwell–Stefan diffusion equations
Correction to: Optimal Estimate of the Spectral Gap for the Degenerate Goldstein-Taylor Model (Journal of Statistical Physics, (2013), 153, 2, (363-375), 10.1007/s10955-013-0825-6)
No full textMathematical and Numerical Study of a Dusty Knudsen Gas Mixture
No full textWe consider a mixture composed of a gas and dust particles in a very rarefied setting. Whereas the dust particles are individually described, the surrounding gas is treated as a Knudsen gas, in such a way that interactions occur only between gas particles and dust by means of diffuse reflection phenomena. After introducing the model, we prove the existence and the uniqueness of the solution and provide a numerical strategy for the study of the equations. At the numerical level, we focus our attention on the phenomenon of energy transfer between the gas and the moving dust particles
Homogenization of the linear Boltzmann equation with a highly oscillating scattering term in extended phase space
No full textIn this article, we rigorously prove the homogenization limit of the linear Boltz-mann equation when the scattering term is highly oscillating with respect to the velocity variable. We prove that the limit equation keeps, in a suitably extended phase space, the same structure as the non-homogenized one. This situation does not coincide with what happens in standard phase space, where the appearance of memory terms is expected. (c) 2023 Elsevier Ltd. All rights reserved
On the Homogenization of the Renewal Equation with Heterogeneous External Constraints
No full textWe study the homogenization limit of the renewal equation with heterogeneous external constraints by means of the two-scale convergence theory. We prove that the homogenized limit satisfies an equation involving non-local terms, which are the consequence of the oscillations in the birth and death terms. We have moreover shown that the numerical approximation of the homogenized equation via the two-scale limit gives an alternative way for the numerical study of the solution of the limiting problem
Mean Field Games of Controls with Dirichlet Boundary Conditions
No full textIn this paper, we study a mean-field games system with Dirichlet boundary conditions in a closed domain and in a mean-field game of controls setting, that is in which the dynamics of each agent is affected not only by the average position of the rest of the agents but also by their average optimal choice. This setting allows the modeling of more realistic real-life scenarios in which agents not only will leave the domain at a certain point in time (like during the evacuation of pedestrians or in debt refinancing dynamics) but also act competitively to anticipate the strategies of the other agents. We shall establish the existence of Nash Equilibria for such class of mean-field game of controls systems under certain regularity assumptions on the dynamics and the Lagrangian cost. Much of the paper is devoted to establishing several a priori estimates which are needed to circumvent the fact that the mass is not conserved (as we are in a Dirichlet boundary condition setting). In the conclusive sections, we provide examples of systems falling into our framework as well as numerical implementations
Compactness of linearized kinetic operators
No full textThis article reviews various results on the compactness of the linearized Boltzmann operator and of its generalization to mixtures of non-reactive monatomic gases
Kinetic approach to the collective dynamics of the rock-paper-scissors binary game
No full textThis article studies the kinetic dynamics of the rock-paper-scissors binary game. We first prove existence and uniqueness of the solution of the kinetic equation and subsequently we prove the rigorous derivation of the quasi-invariant limit for two meaningful choices of the domain of definition of the independent variables. We notice that the domain of definition of the problem plays a crucial role and heavily influences the behavior of the solution. The rigorous proof of the relaxation limit does not need the use of entropy estimates for ensuring compactness
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