316 citations · 1.1k across the 44 of their papers we have counts for
5 papers · 2 filters
One-dimensional inelastic Boltzmann equation: Stability and uniqueness of self-similar -profiles for moderately hard potentials
R. Alonso, V. Bagland, J. A. Cañizo +2
We prove the stability of self-similar profiles under the hard-to-Maxwell potential limit for the one-dimensional inelastic Boltzmann equation with moderately hard potentia…
A uniform-in-time nonlocal approximation of the standard Fokker-Planck equation
José A. Cañizo, Niccolò Tassi
We study a nonlocal approximation of the Fokker-Planck equation in which we can estimate the speed of convergence to equilibrium in a way which does not degenerate as we approach t…
Relaxation in Sobolev spaces and spectral gap of the 1D dissipative Boltzmann equation with Maxwell interactions
R. Alonso, V. Bagland, J. A. Cañizo +2
We study the dynamic relaxation to equilibrium of the 1D dissipative Boltzmann equation with Maxwell interactions in classical Sobolev spaces. In addition, we present a spect…
Sequence of pseudoequilibria describes the long-time behavior of the nonlinear noisy leaky integrate-and-fire model with large delay
María J. Cáceres, José A. Cañizo, Alejandro Ramos-Lora
There is a wide range of mathematical models that describe populations of large numbers of neurons. In this article, we focus on nonlinear noisy leaky integrate-and-fire (NNLIF) mo…
On the asymptotic behavior of the NNLIF neuron model for general connectivity strength
María J. Cáceres, José A. Cañizo, Alejandro Ramos-Lora
We prove new results on the asymptotic behavior of the nonlinear integrate-and-fire neuron model. Among them, we give a criterion for the linearized stability or instability of equ…