10 citations · 43 across the 13 of their papers we have counts for
16 papers
On the singular limit of the Camassa-Holm equation
Billel Guelmame
We study the singular limit of the Camassa--Holm equation as the length scale tends to zero. Although the formal limit is the Burgers equation with flux , we show th…
Strong Ill-Posedness in critical and subcritical regimes for the Hunter-Saxton equation
Billel Guelmame, Haroune Houamed
We study the Hunter--Saxton equation on the real line and its global dissipative solution in the energy space We prove strong ill-p…
A quantitative averaging lemma for spatially dependent vector fields
Paul Alphonse, Billel Guelmame, Julien Vovelle
We prove a quantitative averaging lemma for spatially dependent vector fields. Our proof is based on an iteration of the regularizing operator and some elementary considerations ab…
Singular traveling waves for the Euler-Poisson system
Billel Guelmame, Taoufik Hmidi, Haroune Houamed +1
We consider the Euler-Poisson system for ions where the electrons are given by a Maxwell-Boltzmann distribution, and we investigate the existence of one-dimensional periodic travel…
A Smoluchowski-Kramers approximation for the stochastic variational wave equation
Billel Guelmame, Julien Vovelle
We investigate the Smoluchowski-Kramers approximation for the one-dimensional periodic variational wave equation with state-dependent damping and additive noise. We show that weak…
Convergence rate for a regularized scalar conservation law
Billel Guelmame, Haroune Houamed
This work revisits a recent finding by the first author concerning the local convergence of a regularized scalar conservation law. We significantly improve the original statement b…