139 citations · 631 across the 46 of their papers we have counts for
5 papers · 1 filter
Viscous shock waves of Burgers equation with fast diffusion and singularity
Shufang Xu, Ming Mei, Jean-Christophe Nave +1
In this paper, we study the asymptotic stability of viscous shock waves for Burgers' equation with fast diffusion on when…
Stationary non-radial localized patterns in the planar Swift-Hohenberg PDE: constructive proofs of existence
Matthieu Cadiot, Jean-Philippe Lessard, Jean-Christophe Nave
In this paper, we present a methodology for establishing constructive proofs of existence of smooth, stationary, non-radial localized patterns in the planar Swift-Hohenberg equatio…
Nonlinear stability of shock profiles to Burgers' equation with critical fast diffusion and singularity
Xiaowen Li, Jingyu Li, Ming Mei +1
In this paper we propose the first framework to study Burgers' equation featuring critical fast diffusion in form of . The solution possesses a strong si…
Rigorous computation of solutions of semi-linear PDEs on unbounded domains via spectral methods
Matthieu Cadiot, Jean-Philippe Lessard, Jean-Christophe Nave
In this article we present a general method to rigorously prove existence of strong solutions to a large class of autonomous semi-linear PDEs in a Hilbert space $H^{l}\subset H^{s}…
On "jamitons," self-sustained nonlinear traffic waves
Morris R. Flynn, Aslan R. Kasimov, Jean-Christophe Nave +2
"Phantom jams," traffic blockages that arise without apparent cause, have long frustrated transportation scientists. Herein, we draw a novel homology between phantom jams and a rel…