5 papers
Deriving subdiffusion equations from general Renewal--Jump dynamics
Benoît Perthame, Min Tang
Subdiffusion occurs when long trapping or residence times of particles slow down spatial transport and produce a mean squared displacement proportional to , with~. We d…
A Fokker-Planck equation with superlinear drift at infinity for Integrate-and-Fire model
Benoît Perthame, Clément Rieutord, Delphine Salort
The Integrate-and-Fire model is a Fokker-Planck equation arising in neuroscience. It describes the evolution of the probability density of the neuronal membrane potential and fitti…
Deriving sub-diffusion equations
Benoît Perthame, Min Tang
Sub-diffusion equations are used in a large range of applications including fluids, plasma physics and biology. Their mathematical analysis is advanced even if a much larger litera…
Incompressible limit of porous media equation with chemotaxis and growth
Qingyou He, Hai-Liang Li, Benoît Perthame
We revisit the problem of proving the incompressible limit for the compressible porous media equation with Newtonian drift and growth. The question is motivated by models of living…
An infinite-times renewal equation
Xu'An Dou, Benoît Perthame, Chenjiayue Qi +2
In neuroscience, the time elapsed since the last discharge has been used to predict the probability of the next discharge. Such predictions can be improved taking into account the…