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Nonlinear boundary control of semilinear parabolic problems with pointwise state constraints
1.  Laboratoire MIP, UMR 5640, Université Paul Sabatier, 31062 Toulouse Cedex 4 
[1] 
Evelyn Herberg, Michael Hinze, Henrik Schumacher. Maximal discrete sparsity in parabolic optimal control with measures. Mathematical Control and Related Fields, 2020, 10 (4) : 735759. doi: 10.3934/mcrf.2020018 
[2] 
JeanDaniel Djida, Gisèle Mophou, Mahamadi Warma. Optimal control of mixed localnonlocal parabolic PDE with singular boundaryexterior data. Evolution Equations and Control Theory, 2022, 11 (6) : 21292163. doi: 10.3934/eect.2022015 
[3] 
Shu Luan. On the existence of optimal control for semilinear elliptic equations with nonlinear neumann boundary conditions. Mathematical Control and Related Fields, 2017, 7 (3) : 493506. doi: 10.3934/mcrf.2017018 
[4] 
Piermarco Cannarsa, Patrick Martinez, Judith Vancostenoble. The cost of controlling weakly degenerate parabolic equations by boundary controls. Mathematical Control and Related Fields, 2017, 7 (2) : 171211. doi: 10.3934/mcrf.2017006 
[5] 
Matthias Gerdts, Martin Kunkel. Convergence analysis of Euler discretization of controlstate constrained optimal control problems with controls of bounded variation. Journal of Industrial and Management Optimization, 2014, 10 (1) : 311336. doi: 10.3934/jimo.2014.10.311 
[6] 
William G. Litvinov. Optimal control of electrorheological clutch described by nonlinear parabolic equation with nonlocal boundary conditions. Journal of Industrial and Management Optimization, 2011, 7 (2) : 291315. doi: 10.3934/jimo.2011.7.291 
[7] 
Ugur G. Abdulla. On the optimal control of the free boundary problems for the second order parabolic equations. II. Convergence of the method of finite differences. Inverse Problems and Imaging, 2016, 10 (4) : 869898. doi: 10.3934/ipi.2016025 
[8] 
Alexander Arguchintsev, Vasilisa Poplevko. An optimal control problem by parabolic equation with boundary smooth control and an integral constraint. Numerical Algebra, Control and Optimization, 2018, 8 (2) : 193202. doi: 10.3934/naco.2018011 
[9] 
Eduardo Casas, Konstantinos Chrysafinos. Analysis and optimal control of some quasilinear parabolic equations. Mathematical Control and Related Fields, 2018, 8 (3&4) : 607623. doi: 10.3934/mcrf.2018025 
[10] 
Rajae Aboulaϊch, Amel Ben Abda, Moez Kallel. Missing boundary data reconstruction via an approximate optimal control. Inverse Problems and Imaging, 2008, 2 (4) : 411426. doi: 10.3934/ipi.2008.2.411 
[11] 
Hongyong Deng, Wei Wei. Existence and stability analysis for nonlinear optimal control problems with $1$mean equicontinuous controls. Journal of Industrial and Management Optimization, 2015, 11 (4) : 14091422. doi: 10.3934/jimo.2015.11.1409 
[12] 
Domingo Tarzia, Carolina Bollo, Claudia Gariboldi. Convergence of simultaneous distributedboundary parabolic optimal control problems. Evolution Equations and Control Theory, 2020, 9 (4) : 11871201. doi: 10.3934/eect.2020045 
[13] 
Ugur G. Abdulla, Evan Cosgrove, Jonathan Goldfarb. On the Frechet differentiability in optimal control of coefficients in parabolic free boundary problems. Evolution Equations and Control Theory, 2017, 6 (3) : 319344. doi: 10.3934/eect.2017017 
[14] 
Dung Le. Strong positivity of continuous supersolutions to parabolic equations with rough boundary data. Discrete and Continuous Dynamical Systems, 2015, 35 (4) : 15211530. doi: 10.3934/dcds.2015.35.1521 
[15] 
Volodymyr O. Kapustyan, Ivan O. Pyshnograiev, Olena A. Kapustian. Quasioptimal control with a general quadratic criterion in a special norm for systems described by parabolichyperbolic equations with nonlocal boundary conditions. Discrete and Continuous Dynamical Systems  B, 2019, 24 (3) : 12431258. doi: 10.3934/dcdsb.2019014 
[16] 
Ugur G. Abdulla. On the optimal control of the free boundary problems for the second order parabolic equations. I. Wellposedness and convergence of the method of lines. Inverse Problems and Imaging, 2013, 7 (2) : 307340. doi: 10.3934/ipi.2013.7.307 
[17] 
N. Arada, J.P. Raymond. Time optimal problems with Dirichlet boundary controls. Discrete and Continuous Dynamical Systems, 2003, 9 (6) : 15491570. doi: 10.3934/dcds.2003.9.1549 
[18] 
Hongwei Lou, Jiongmin Yong. Secondorder necessary conditions for optimal control of semilinear elliptic equations with leading term containing controls. Mathematical Control and Related Fields, 2018, 8 (1) : 5788. doi: 10.3934/mcrf.2018003 
[19] 
C. García Vázquez, Francisco Ortegón Gallego. On certain nonlinear parabolic equations with singular diffusion and data in $L^1$. Communications on Pure and Applied Analysis, 2005, 4 (3) : 589612. doi: 10.3934/cpaa.2005.4.589 
[20] 
Rosaria Di Nardo. Nonlinear parabolic equations with a lower order term and $L^1$ data. Communications on Pure and Applied Analysis, 2010, 9 (4) : 929942. doi: 10.3934/cpaa.2010.9.929 
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