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Global stabilization of viscous Burgers' equation around constant steadystate solution has been discussed in the literature. The main objective of thispaper is to show global stabilization results for the 2D forced viscousBurgers' equation around a nonconstant steady state solution using nonlinearNeumann boundary feedback control law, under some smallness condition on thatsteady state solution. On discretizing in space using $C^0$ piecewise linearelements keeping time variable continuous, a semidiscrete scheme is obtained.Moreover, global stabilization results for the semidiscrete solution andoptimal error estimates for the state variable in $L^\infty(L^2)$ and$L^\infty(H^1)$-norms are derived. Further, optimal convergence result isestablished for the boundary feedback control law. All our results in thispaper preserve exponential stabilization property. Finally, some numericalexperiments are documented to confirm our theoretical findings.

Global Stabilization of 2D Forced Viscous Burgers' Equation Around  Nonconstant Steady State Solution by Nonlinear Neumann Boundary Feedback  Control:Theory and Finite Element Analysis