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تسجيل مستخدم جديدGlobal Stabilization of Two Dimensional Viscous Burgers Equation by Nonlinear Neumann Boundary Feedback Control and its Finite Element Analysis
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In this article, global stabilization results for the two dimensional (2D) viscous Burgers equation, that is, convergence of unsteady solution to its constant steady state solution with any initial data, are established using a nonlinear Neumann boundary feedback control law. Then, applying $C^0$-conforming finite element method in spatial direction, optimal error estimates in $L^infty(L^2)$ and in $L^infty(H^1)$- norms for the state variable and convergence result for the boundary feedback control law are derived. All the results preserve exponential stabilization property. Finally, several numerical experiments are conducted to confirm our theoretical findings.
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Global stabilization of viscous Burgers equation around constant steady state solution has been discussed in the literature. The main objective of this paper is to show global stabilization results for the 2D forced viscous Burgers equation around a
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