Nejib Smaoui

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We investigate analytically as well as numerically Burgers equation with a high-order nonlinearity (i.e., u t = νu xx − u n u x + mu + h(x)). We show existence of an absorbing ball in L 2 [0, 1] and uniqueness of steady state solutions for all integer n ≥ 1. Then, we use an adaptive nonlinear boundary controller to show that it guarantees global asymptotic(More)
We study numerically the long-time dynamics of a system of reaction-diffusion equations that arise from the viscous forced Burgers equation (u + uu x-uuxx F). A nonlinear transformation introduced by Kwak is used to embed the scalar Burgers equation into a system of reaction diffusion equations. The Kwak transformation is used to determine the existence of(More)
A hybrid approach consisting of two neural networks is used to model the oscillatory dy-namical behavior of the Kuramoto-Sivashinsky (KS) equation at a bifurcation parameter α = 84.25. This oscillatory behavior results from a fixed point that occurs at α = 72 having a shape of two-humped curve that becomes unstable and undergoes a Hopf bifurcation at α =(More)
Keywords: Two-dimensional Navier–Stokes equations Bifurcations Dynamical systems and control a b s t r a c t This paper deals with the dynamics and control of the two-dimensional (2-d) Navier– Stokes (N–S) equations with a spatially periodic and temporally steady forcing term. First, we construct a dynamical system of nine nonlinear differential equations(More)