BOUNDARY FEEDBACK STABILIZATION OF BOUSSINESQ EQUATIONS

Abstract

Abstract: The aim of this work is to design oblique boundary feedback controller for stabilizing the equilibrium solutions to Boussinesq equations on a bounded and open domain in R². Two kinds of such feedback controller are provided, one is the proportional stabilizable feedback control, which is obtained by spectrum decomposition method, while another one is constructed via the Ricatti operator for an infinite time horizon optimal control problem. An example of periodic Boussinesq flow in 2-D channel is also given.

Key words: Boussinesq equations, boundary feedback controller, eigenvalue

Hanbing LIU, Haijun XIAO. BOUNDARY FEEDBACK STABILIZATION OF BOUSSINESQ EQUATIONS[J].Acta mathematica scientia,Series B, 2018, 38(6): 1881-1902.

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