9 papers · 1 filter
Self-similarity and diffusive limits for linear kinetic equations: a Wild sum approach
José A. Cañizo, Stéphane Mischler, Niccolò Tassi
We prove that linear collisional kinetic equations in the whole space without confinement mechanism display a long-time self-similar behaviour. This drastically improves the recent…
Sharp asymptotic behaviour of symmetric and non-symmetric solutions of the Heat Equation in the Hyperbolic Space
José Alfredo Cañizo, Alejandro Gárriz, Diego Alfonso MarÃn
In this work we study the large-time behaviour of solutions of the Heat Equation in the hyperbolic space , providing precise speeds of convergence in and $L^\in…
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…
Comparison principles and asymptotic behavior of delayed age-structured neuron models
MarÃa J Cáceres, José A Cañizo, Nicolas Torres
In the context of neuroscience the elapsed-time model is an age-structured equation that describes the behavior of interconnected spiking neurons through the time since the last di…
Large-time estimates for the Dirichlet heat equation in exterior domains
José A. Cañizo, Alejandro Gárriz, Fernando Quirós
We give large-time asymptotic estimates, both in uniform and norms, for solutions of the Dirichlet heat equation in the complement of a bounded open set of sat…
Sequence of pseudoequilibria describes the long-time behavior of the nonlinear noisy leaky integrate-and-fire model with large delay
MarÃa 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…