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)
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)
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)