Nejib Smaoui

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The Karhunen–Loève (K–L) analysis is widely used to generate low-dimensional dynamical systems, which have the same low-dimensional attractors as some large-scale simulations of PDEs. If the PDE is symmetric with respect to a symmetry group G, the dynamical system has to be equivariant under G to capture the full phase space. It is shown that symmetrizing(More)
We investigate analytically as well as numerically Burgers equation with a high-order nonlinearity (i.e., ut = νuxx−unux+mu+h(x)). We show existence of an absorbing ball in L2[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 stability in(More)
This paper proposes an improved image encryption scheme over existing scheme. The distinct feature of improved encryption scheme is that it encrypts the image using chaotic maps only without further confusing this encrypted image as illustrated in existing scheme. Further, the advantages over existing scheme are 1) the proposed algorithm is completely(More)
We study numerically the long-time dynamics of a system of reaction-diffusion equations that arise from the viscous forced Burgers equation (u + uux -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)
We consider the generalized Burgers equation with and without a time delay when the boundary conditions are periodic with period 2π. For the generalized Burgers equation without a time delay, that is, ut = νuxx − uux + u+ h(x), 0 < x < 2π, t > 0, u(0, t) = u(2π, t), u(x,0) = u0(x), a Lyapunov function method is used to show boundedness and uniqueness of a(More)