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math.AP2024
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…
math.AP2024★ 10 cited
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…
math.AP2024★ 1 cited
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…