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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)

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)

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