10 citations · 43 across the 13 of their papers we have counts for
11 papers · 1 filter
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…