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Fractional diffusion limit for collisional kinetic equations
fractional diffusion fractional heat equation anomalous heat transport linear Boltzmann equation relaxation equation linear BGK equation diffusion limit anomalous diffusion limit anomalous diffusive time scale mathematical derivation
2015/10/15
This paper is devoted to diffusion limits of linear Boltzmann equations. When the equilibrium distribution function is a Maxwellian distribution, it is well known that for an appropriate time scale, t...
Fractional diffusion limit for collisional kinetic equations:A moments method
Kinetic equations linear Boltzmann equation asymptotic analysis diffusion limit anomalous diffusion limit fractional diffusion relaxation equation anomalous diffusive time scale
2015/10/15
This paper is devoted to hydrodynamic limits of linear kinetic equations. We consider situations in which the thermodynamical equilibrium is described by a heavy-tail distribution function rather than...
Anomalous diffusion limit for kinetic equations with degenerate collision frequency
Anomalous diffusion limit kinetic equations degenerate collision frequency
2015/10/15
This paper is devoted to hydrodynamic limits for collisional linear kinetic equations. It is a classical result that under certain conditions on the collision operator, the long time/small mean free p...
Fractional diffusion limit for collisional kinetic equations:a Hilbert expansion approach
Fractional diffusion limit collisional kinetic equations Hilbert expansion
2015/10/15
We develop a Hilbert expansion approach for the derivation of fractional diffusion equations from the linear Boltzmann equation with heavy tail equilibria.
Stochastic averaging lemmas for kinetic equations
Stochastic kinetic equations stochastic conservation laws averaging lemmas fractional Sobolev spaces
2012/4/17
We develop a class of averaging lemmas for stochastic kinetic equations. The velocity is multiplied by a white noise which produces a remarkable change in time scale. Compared to the deterministic cas...
Chemotaxis: from kinetic equations to aggregate dynamics
duality solutions non local conservation equations hydrodynamic limit measure-valued solutions chemotaxis
2011/8/25
Abstract: The hydrodynamic limit for a kinetic model of chemotaxis is investigated. The limit equation is a non local conservation law, for which finite time blow-up occurs, giving rise to measure-val...
A boundary matching micro/macro decomposition for kinetic equations
boundary matching micro/macro decomposition kinetic equations
2011/1/21
We introduce a new micro/macro decomposition of collisional kinetic equations which naturally incorporates the exact space boundary conditions.
World leaders from diverse branches of kinetic theory will gather for an intense two-day workshop at the University of Victoria in April, 2007. Ten invited speakers will deliver hour-long lectures on ...