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Bang-bang property of time optimal controls of semilinear parabolic equation

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  • The bang-bang property of time optimal controls for a semilinear parabolic equation, with homogeneous Dirichlet boundary condition and distributed controls acting on an open subset of the domain is established. This relies on an observability estimate from a measurable set in time for a linear parabolic equation, with potential depending on both space and time variables. The proof of the bang-bang property relies on a Kakutani fixed point argument.
    Mathematics Subject Classification: Primary: 35K10, 49J20; Secondary: 49J30, 93B07.


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  • [1]

    V. Barbu, Analysis and Control of Nonlinear Infinite Dimensional Systems, Academic Press, Boston, 1993.


    V. Barbu, The time optimal control of Navier-Stokes equations, Systems Control Lett., 30 (1997), 93-100.doi: 10.1016/S0167-6911(96)00083-7.


    H. O. Fattorini, Time optimal control of solutions of operational differential equations, J. SIAM Control, 2 (1964), 54-59.doi: 10.1137/0302005.


    H. O. Fattorini, Infinite Dimensional Linear Control Systems: The Time Optimal and Norm Optimal Problems, North-Holland Mathematics Studies 201, ELSEVIER, 2005.


    K. Kunisch and L. J. Wang, Time optimal controls of the linear Fitzhugh-Nagumo equation with pointwise control constraints, J. Math. Anal. Appl., 395 (2012), 114-130.doi: 10.1016/j.jmaa.2012.05.028.


    K. Kunisch and L. J. Wang, Time optimal control of the heat equation with pointwise control constraints, ESAIM: Control Optim. Calc. Var., 19 (2013), 460-485.doi: 10.1051/cocv/2012017.


    K. Kunisch and L. J. Wang, Bang-bang property of time optimal controls of Burgers equation, Discrete Contin. Dyn. Syst., 34 (2014), 3611-3637.doi: 10.3934/dcds.2014.34.3611.


    O. A. Ladyženskaja, V. A. Solonnikov and N. N. Ural’ceva, Linear and Quasilinear Equations of parabolic Type, American Mathematical Society, 1968.


    J. L. Lions, Optimal Control of Systems Governed by Partial Differential Equations, Springer, Berlin, 1971.


    V. J. Mizel and T. I. Seidman, An abstract bang-bang principle and time optimal boundary control of the heat equation, SIAM J. Control Optim., 35 (1997), 1204-1216.doi: 10.1137/S0363012996265470.


    K. D. Phung and G. Wang, Quantitative unique continuation for the semilinear heat equation in a convex domain, J. Funct. Anal., 259 (2010), 1230-1247.doi: 10.1016/j.jfa.2010.04.015.


    K. D. Phung, L. J. Wang and C. Zhang, Bang-bang property for time optimal control of semilinear heat equation, Ann. Inst. H. Poincaré Anal. Non Linéaire, 31 (2014), 477-499.doi: 10.1016/j.anihpc.2013.04.005.


    G. S. Wang, $L^\infty$-null controllability for the heat equtaion and its consequences for the time optimal control problem, SIAM J. Control Optim., 47 (2008), 1701-1720.doi: 10.1137/060678191.


    G. S. Wang and L. J. Wang, The Bang-Bang principle of time optimal controls for the heat equation with internal controls, Systems Control Lett., 56 (2007), 709-713.doi: 10.1016/j.sysconle.2007.06.001.


    L. J. Wang and G. S. Wang, The optimal time control of a phase-field system, SIAM J. Control Optim., 42 (2003), 1483-1508.doi: 10.1137/S0363012902405455.

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