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…
On a Hamiltonian regularization of scalar conservation laws
Billel Guelmame
In this paper, we propose a Hamiltonian regularization of scalar conservation laws, which is parametrized by and conserves an energy. We prove the existence of glo…
Global weak solutions of the Serre-Green-Naghdi equations with surface tension
Billel Guelmame
We consider in this paper the Serre--Green--Naghdi equations with surface tension. Smooth solutions of this system conserve an -equivalent energy. We prove the existence of gl…
On the blow-up scenario for some modified Serre-Green-Naghdi equations
Billel Guelmame
The present paper deals with a modified Serre-Green-Naghdi (mSGN) system that has been introduced by Clamond et al. to improve the dispersion relation. We present a precise blow-up…
Global dissipative martingale solutions to the variational wave equation with stochastic forcing
Billel Guelmame, Julien Vovelle
We consider the variational wave equation in one-dimensional space with stochastic forcing by an additive noise. Blow-up of local smooth solutions is established, and global existe…
Entropy solutions in for a class of triangular systems involving a transport equation
Christian Bourdarias, Anupam Pal Choudhury, Billel Guelmame +1
In this article, we consider a class of strictly hyperbolic triangular systems involving a transport equation. Such systems are known to create measure solutions for the initial va…
Global weak solutions of a Hamiltonian regularised Burgers equation
Billel Guelmame, Stéphane Junca, Didier Clamond +1
A nondispersive, conservative regularisation of the inviscid Burgers equation is proposed and studied. Inspired by a related regularisation of the shallow water system recently int…
Local well-posedness of a Hamiltonian regularisation of the Saint-Venant system with uneven bottom
Billel Guelmame, Didier Clamond, Stéphane Junca
We prove in this note the local (in time) well-posedness of a broad class of symmetrisable hyperbolic system involving additional non-local terms. The latest result im…
Hamiltonian regularisation of the unidimensional barotropic Euler equations
Billel Guelmame, Didier Clamond, Stéphane Junca
Recently, a Hamiltonian regularised shallow water (Saint-Venant) system has been introduced by Clamond and Dutykh. This system is Galilean invariant, linearly non-dispersive and co…
Optimal regularity for all time for entropy solutions of conservation laws in
Shyam Sundar Ghoshal, Billel Guelmame, Animesh Jana +1
This paper deals with the optimal regularity for entropy solutions of conservation laws. For this purpose, we use two key ingredients: (a) fine structure of entropy solutions and (…
Regularizing effect for conservation laws with a Lipschitz convex flux
Billel Guelmame, Stéphane Junca, Didier Clamond
This paper studies the smoothing effect for entropy solutions of conservation laws with general nonlinear convex fluxes on . Beside convexity, no additional regularity…