[1] Ladyzenskaya O A, Solonnikov V A, Uraltseva N N. Linear and Quasilinear Equations of Parabolic Type. Providence: Amer Math Soc Translation, 1968
[2] Imanuvilov O Y, Yamamoto M. Carleman inequalities for parabolic equations in sobolev space of negative order and exact controllability for semilinear parabblic equations. Publ Res Inst Math Sci, 2003, 39(2): 227--274
[3] Wang G S, Wang L J. The Carleman inequality and its application to periodic optimal control governed by semilinear parabolic differential equations. Journal of Optimization Theory and Appllications, 2003, 118: 429--461
[4] Zuazua E. Approximate controllability for semilinear heat equations with global Lipschitz nonlinearities. Control and Cybernetics, 1999,
28(3): 665--683
[5] Doubova A E, Fernàndez-cara E M, Gonzàlez-bvrgos M, Zuazua E. On the controllability of parabolic systems with a nonlinear term involving the state and the gradient. SIAM J Con Opt, 2002, 41(3): 798--819
[6] Ammar Khodja F, Benabdallah A, Dupaix C, Kostin I. Controllability to the trajectories of phase-field models by one control force. SIAM J Control Optimal, 2003, 42: 1661--1680
[7] Wang G S, Zhang L. Exact local controllability of a one-control reaction-diffusion system. Journal of Optimization Theory and Appllications, 2006, 131(3): 453--467
[8] Fu X Y, Zhang X, Zuazua E. On the Optimality of Some Observability Inequalities for Plate Systems with Potentials. Proceedings of the
Conference “Phase Space Analysis and PDE”. Pienza: Birkhauser, 2005: 117--132 |