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Neumann boundary optimal control problems governed by parabolic variational equalities


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Ben Belgacem, F., El Fekih, H. and Raymond, J. P. (2003) A penalized Robin approach for solving a parabolic equation with nonsmooth Dirichlet boundary conditions. Asymptotic Anal., 34, 121–136. Search in Google Scholar

Bergounioux, M. and Tröltzsch, F. (1999) Optimal control of semilinear parabolic equations with state-constraints of Bottleneck type. ESAIM: Control, Optim. Calc. Var. 4, 595–608.10.1051/cocv:1999124 Search in Google Scholar

Boukrouche, M. and Tarzia, D. A. (2013) Convergence of optimal control problems governed by second kind parabolic variational inequalities. J. Control Theory Appl. 11, 422–427.10.1007/s11768-013-2155-2 Search in Google Scholar

Brézis, H. (1972) Problèmes unilatéraux. Journal de Mathématiques Pures et Appliquées, 51(1), 1–162. Search in Google Scholar

Chrysafinos, K., Gunzburger, M. D. and Hou L. S. (2006) Semidiscrete approximations of optimal Robin boundary control problems constrained by semilinear parabolic PDE. J. Math. Anal. Appl. 323, 891–912.10.1016/j.jmaa.2005.10.053 Search in Google Scholar

Chrysafinos, K. and Hou, L. S. (2017) Analysis and approximations of the evolutionary Stokes equations with inhomogeneous boundary and divergence data using a parabolic saddle point formulation. ESAIM: Mathematical Modelling and Numerical Analysis 51, 1501–1526.10.1051/m2an/2016070 Search in Google Scholar

Duvaut, G. and Lions, J. L. (1972) Les inéquations en mécanique et en physique. Paris: Dunod. Search in Google Scholar

Gariboldi, C. M. and Tarzia, D. A. (2008) Convergence of boundary optimal control problems with restrictions in mixed elliptic Stefan-like problems. Adv. in Diff. Eq. and Control Processes, 1(2), 113-132. Search in Google Scholar

Gariboldi, C. M. and Tarzia, D. A. (2015) Existence, uniqueness and convergence of simultaneous distributed-boundary optimal control problems. Control and Cybernetics, 44, 5–17. Search in Google Scholar

Gonzalez, R. L. V. and Tarzia, D. A. (1990) Optimization of heat flux in domains with temperature constraints. Journal of Optimization Theory and Applications, 65(2), 245–256.10.1007/BF01102344 Search in Google Scholar

Gunzburger, M. D. and Hou, S. L. (1992) Treating inhomogeneous essential boundary conditions in finite element methods and the calculation of boundary stresses. SIAM J. Numer. Anal. 29(2), 390–424.10.1137/0729024 Search in Google Scholar

Kinderleher, D. and Stampacchia, G. (2000) An Introduction to Variational Inequalities and Their Applications. SIAM, Philadelphia.10.1137/1.9780898719451 Search in Google Scholar

Lions, J.L. (1968) Contrôle optimal de systèmes gouvernés par des équations aux drives partielles. Dunod, Paris. Search in Google Scholar

Menaldi, J. and Tarzia, D. A. (2007) A distributed parabolic control with mixed boundary conditions. Asymptotic Analysis 52, 227–241. Search in Google Scholar

Sener, S. S. and Subasi, M. (2015) On a Neumann boundary control in a parabolic system. Boundary Value Problems, 2015:166, 1–12.10.1186/s13661-015-0430-5 Search in Google Scholar

Sweilam, N. H. and Abd-Elal, L. F. (2003) A computational approach for optimal control systems goberned by parabolic variational inequalities. Journal of Computational Mathematics 21:6, 815–824. Search in Google Scholar

Tarzia, D. A., Bollo, C. M. and Gariboldi, C. M. (2020) Convergence of simultaneous distributed-boundary parabolic optimal control problems. Evolution Equations and Control Theory. 9(4), 1187–1201.10.3934/eect.2020045 Search in Google Scholar

Tröltzsch, F. (2010) Optimal Control of Partial Differential Equations. Theory, Methods and Applications. American Math. Soc., Providence.10.1090/gsm/112/07 Search in Google Scholar

Wang, L. and Yan, Q. (2019) Optimal control problem for exact synchronization of parabolic system. Mathematical Control and Related Fields 9(3), 411–424.10.3934/mcrf.2019019 Search in Google Scholar