8 documents found, page 1 of 1
Travelling waves in a dispersion–saturating diffusion equation
Maypaokha, Gnord; Bedjaoui, Nabil; Grinfeld, Michael; Correia, Joaquim M.C.In the framework of hyperbolic conservation laws regularised by including diffusive and dispersive terms, we study monotone travelling waves for the generalised Rosenau–Korteweg de Vries equation. We establish existence as well as linear and nonlinear determinacy results in different regimes.; ISP (International Science programme), Uppsala University, Sweden; EMS (Edinburgh Mathematical Society), Edinburgh, UK;...
On a limit of perturbed conservation laws with saturating diffusion and non-pos...
Bedjaoui, Nabil; Correia, Joaquim M.C.; Mammeri, YoucefWe consider a conservation law with convex flux, perturbed by a saturating diffusion and non-positive dispersion of the form $u_t + f(u)_x = ε(u_x/\sqrt{1+u_x^2})_x − δ(|u_xx|^n)_x$. We prove the convergence of the solutions $u^{ε,δ}$ to the entropy weak solution of the hyperbolic conservation law, $u_t + f(u)_x = 0$, for all real number $1 ≤ n ≤ 2$ provided $δ = o(ε^{n(n+1)/2};ε^{n+1/n})$.; PICS 2018/8262 (201...
Traffic Modelling and Some Inequalities in Banach Spaces
Bedjaoui, Nabil; Correia, Joaquim; Sirisack, Sackmone; Doungsavanh, BouasyModelling traffic flow has been around since the appearance of traffic jams. Ideally, if we can correctly predict the behavior of vehicle flow given an initial set of data, then adjusting the flow in crucial areas can maximize the overall throughput of traffic along a stretch of road. We consider a mathematical model for traffic flow on single land and without exits or entries. So, we are just observing what ha...
Convergence of a family of perturbed conservation laws with diffusion and non-p...
Bedjaoui, Nabil; Correia, Joaquim M.C.; Mammeri, YoucefWe consider a family of conservation laws with convex flux perturbed by vanishing diffusion and non-positive dispersion of the form u_t + f(u)_x = ε u_xx − δ(|u_xx|^n)_x. Convergence of the solutions {u^(ε,δ)} to the entropy weak solution of the hyperbolic limit equation u_t + f(u)_x = 0, for all real numbers 1 ≤ n ≤ 2 is proved if δ = o(ε^(3n−1)/2 ; ε^(5n−1)/2(2n−1) ).
On a Limit of Perturbed Conservation Laws with Diffusion and Non-Positive Dispe...
Bedjaoui, Nabil; Correia, Joaquim M.C.; Mammeri, YoucefWe consider a conservation law perturbed by a linear diffusion and a general form of non-positive dispersion. We prove the convergence of the corresponding solution to the entropy weak solution of the hyperbolic conservation law.; N/A
Well-Posedness of the Generalized Korteweg-de Vries-Burgers Equation with Nonli...
Bedjaoui, Nabil; Correia, Joaquim; Mammeri, YoucefWe prove the well-posedness of the generalized Korteweg-de Vries-Burgers equation with nonlinear dispersion and nonlinear dissipation ut+f(u)x−δg(uxx)x−εh(ux)x=0. Contrary the linear case, the dispersion properties of the free evolution are useless and a vanishing parabolic regularization is then used.; FCT, UID/MAT/04674/2013
On Vanishing dissipative-dispersive perturbations of hyperbolic conservation laws
Correia, Joaquim M.C.; Bedjaoui, Nabil; Mammeri, YoucefIn presence of linear diffusion and non-positive dispersion, we prove well-posedness of the nonlinear conservation equation u_t+f(u)_x=\eps u_xx -\del((u_xx)^2)_x. Then, as the right-hand perturbations vanish, we prove convergence of the previous solutions to the entropy weak solution of the hyperbolic conservation law u_t+f(u)_x=0.
A note on nonlinear KdV-type equations
Bedjaoui, Nabil; Correia, Joaquim M.C.We consider the approximation of the inviscid Burgers equation by nonlinear Korteweg-de Vries (KdV) type equations. It has been conjectured by Brenier and Levy [1] that in some special kind of nonlinear dispersion the behaviour is dissipative, when generally we expect a dispersive behaviour as in the linear case. We provide here a priori estimates enough to establish the first step in a proof of the conjecture ...