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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...
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.
A Second Order Finite Difference-Spectral Method for Space Fractional Diffusion Equation
A Second Order Finite Difference-Spectral Method Space Fractional Diffusion Equation
2012/8/7
A high order finite difference-spectral method is derived for solving space fractional diffusion equations, by combining the second order finite difference method in time and the spectral Galerkin met...
The influence of fractional diffusion in Fisher-KPP equations
influence fractional diffusion Fisher-KPP equations
2012/2/29
We study the Fisher-KPP equation where the Laplacian is replaced by the generator of a Feller semigroup with power decaying kernel, an important example being the fractional Laplacian. In contrast wit...
On the differentiability of the solution to an equation with drift and fractional diffusion
differentiability solution equation drift fractional diffusion
2011/1/20
We consider an equation with drift and either critical or supercritical fractional diffusion.
Under a regularity assumption for the vector field that is marginally stronger than what is required for ...
Holder estimates for advection fractional-diffusion equations
Holder estimates advection fractional-diffusion equations
2010/12/14
We analyse conditions for an evolution equation with a drift and fractional diffusion to have a H¨older continuous solution. In case the diffusion is of order one or more, we obtain H¨older estimates ...