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Piecewise optimal distributed Controls for 2D Boussinesq equations
Author(s) -
Lee HyungChun,
Shin Byeong Chun
Publication year - 2000
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(200002)23:3<227::aid-mma112>3.0.co;2-5
Subject(s) - piecewise , mathematics , exponential growth , optimal control , exponential function , dynamics (music) , tracking (education) , mathematical analysis , zero (linguistics) , control theory (sociology) , control (management) , mathematical optimization , computer science , physics , psychology , pedagogy , linguistics , philosophy , artificial intelligence , acoustics
In this article, we study the dynamics of a piecewise (in time) distributed optimal control problem for the Boussinesq equations which model velocity tracking over time coupled to thermal dynamics. We also study the dynamics of semidiscrete approximation of this problem. We prove that the rates of velocity tracking coupled to thermal dynamics are exponential and that the difference between the solution of the semi‐discrete piecewise optimal control problem and the desired states in L 2 and H 1 norms decay to zero exponentially as n →∞. Copyright © 2000 John Wiley & Sons, Ltd.