References
- Amann H. Parabolic evolution equations and nonlinear boundary conditions. J Differ Equ. 1988;72:201–269.
- Arrieta JM, Carvalho AN, Rodriguez-Bernal A. Parabolic problems with nonlinear boundary conditions and critical nonlinearities. J Differ Equ. 1999;156:376–406.
- Fernández-Cara E, González-Burgos M, Guerrero S, et al. Exact controllability to the trajectories of the heat equation with Fourier boundary conditions: the semilinear case. ESAIM Control Optim Calc Var. 2006;12(3):466–483. DOI:10.1051/cocv:2006011
- Fernández-Cara E, González-Burgos M, Guerrero S, et al . Null controllability of the heat equation with boundary fourier conditions: the linear case. ESAIM Control Optim Calc Var. 2006;12(3):442–465.
- Grisvard P. Contrôlabilité exacte des solutions de l’équation des ondes en présence de singularités. J Math Pures Appl. 1989;68(2):215–259.
- Fursikov AV, Imanuvilov OY. Controllability of evolution equations. Vol. 34. Lecture notes series. Seoul: Research Institute of Mathematics, Global Analysis Research Center, Seoul National University; 1996.
- Barbu V. Controllability of parabolic and Navier--Stokes equations. Sci Math Jpn. 2002;56(1):143–211.
- Fernández-Cara E, Zuazua E. The cost of approximate controllability for heat equations: the linear case. Adv Differ Equ. 2000;5(4–6):465–514.
- Lebeau G, Robbiano L. Contrôle exacte de l’équation de la chaleur. Séminaire sur les Équations aux Dérivées Partielles, 1994--1995. Palaiseau: École Polytech; 1995. p. Exp. No. VII, 13.
- Russell DL. A unified boundary controllability theory for hyperbolic and parabolic partial differential equations. Stud Appl Math. 1973;52:189–211.
- Fernández-Cara E, Guerrero S. Global Carleman inequalities for parabolic systems and application to controllability. SIAM J Control Optim. 2006;45(4):1395–1446.
- Bourgeois L. A stability estimate for ill-posed elliptic cauchy problems in a domain with corners. C R Acad Sci Paris, Ser. 2007;I(345):385–390.
- Belghazi AH, Smadhi F, Zaidi N, et al . Carleman inequalities for the heat equation in singular domains. C R Acad Sci Paris, Ser I. 2010;348(5–6):277–282.
- Cornilleau P, Robbiano L. Carleman estimates for the Zaremba boundary condition and stabilization of waves. Amer J Math. 2014;136(2):393–444. DOI:10.1353/ajm.2014.0014
- Fu X. Logarithmic decay of hyperbolic equations with arbitrary small boundary damping. Commun Partial Differ Equ. 34(7–9):957–975. DOI: 10.1080/03605300903116389
- Aniţa S, Barbu V. Null controllability of nonlinear convective heat equations. ESAIM Control Optim Calc Var. 2000;5:157–173. DOI:10.1051/cocv:2000105
- Doubova A, Osses A, Puel JP. Exact controllability to trajectories for semilinear heat equations with discontinuous diffusion coefficients. ESAIM Control Optim Calc Var. 2002;8:621–661. DOI:10.1051/cocv:2002047
- Fabre C, Puel JP, Zuazua E. Approximate controllability of the semilinear heat equation. Proc Roy Soc Edinb Sec A. 1995;125(1):31–61. DOI:10.1017/S0308210500030742
- Zuazua E. Finite-dimensional null controllability for the semilinear heat equation. J Math Pures Appl. 1997;76(3):237–264. DOI:10.1016/S0021-7824(97)89951-5
- Zuazua E. Approximate controllability of the semilinear heat equation: boundary control. In: Bristeau MO, et al. , editors. Computational science for the 21st century. John Wiley & Sons; 1997. p. 738–747.
- Fernández-Cara E, Zuazua E. Null and approximate controllability for weakly blowing up semilinear heat equations. Ann Inst H Poincaré Anal Non Linéaire. 2000;17(5):583–616. DOI:10.1016/S0294-1449(00)00117-7
- Doubova A, Fernández-Cara E, González-Burgos M. On the controllability of the heat equation with nonlinear boundary Fourier conditions. J Differ Equ. 2004;196(2):385–417. DOI:10.1016/j.jde.2003.09.002
- AliZiane T, Ouzzane H, Zair O. A Carleman estimate for the two dimensional heat equation with mixed boundary conditions. C R Math Acad Sci Paris. 2013;351(3-4):97–100. DOI:10.1016/j.crma.2013.02.006
- Zuazua E. Exact boundary controllability for the semilinear wave equation. Nonlinear partial differential equations and their applications. Collège de France Seminar, Vol. X (Paris, 1987--1988). Vol. 220. Pitman research notes in mathematics series. Harlow: Longman Science and Technology; 357–391.