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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 & Related Fields, 2020, 10 (4) : 735-759. doi: 10.3934/mcrf.2020018 |
[2] |
Shu Luan. On the existence of optimal control for semilinear elliptic equations with nonlinear neumann boundary conditions. Mathematical Control & Related Fields, 2017, 7 (3) : 493-506. doi: 10.3934/mcrf.2017018 |
[3] |
Piermarco Cannarsa, Patrick Martinez, Judith Vancostenoble. The cost of controlling weakly degenerate parabolic equations by boundary controls. Mathematical Control & Related Fields, 2017, 7 (2) : 171-211. doi: 10.3934/mcrf.2017006 |
[4] |
Matthias Gerdts, Martin Kunkel. Convergence analysis of Euler discretization of control-state constrained optimal control problems with controls of bounded variation. Journal of Industrial & Management Optimization, 2014, 10 (1) : 311-336. doi: 10.3934/jimo.2014.10.311 |
[5] |
William G. Litvinov. Optimal control of electrorheological clutch described by nonlinear parabolic equation with nonlocal boundary conditions. Journal of Industrial & Management Optimization, 2011, 7 (2) : 291-315. doi: 10.3934/jimo.2011.7.291 |
[6] |
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 & Imaging, 2016, 10 (4) : 869-898. doi: 10.3934/ipi.2016025 |
[7] |
Alexander Arguchintsev, Vasilisa Poplevko. An optimal control problem by parabolic equation with boundary smooth control and an integral constraint. Numerical Algebra, Control & Optimization, 2018, 8 (2) : 193-202. doi: 10.3934/naco.2018011 |
[8] |
Eduardo Casas, Konstantinos Chrysafinos. Analysis and optimal control of some quasilinear parabolic equations. Mathematical Control & Related Fields, 2018, 8 (3&4) : 607-623. doi: 10.3934/mcrf.2018025 |
[9] |
Rajae Aboulaϊch, Amel Ben Abda, Moez Kallel. Missing boundary data reconstruction via an approximate optimal control. Inverse Problems & Imaging, 2008, 2 (4) : 411-426. doi: 10.3934/ipi.2008.2.411 |
[10] |
Hongyong Deng, Wei Wei. Existence and stability analysis for nonlinear optimal control problems with $1$-mean equicontinuous controls. Journal of Industrial & Management Optimization, 2015, 11 (4) : 1409-1422. doi: 10.3934/jimo.2015.11.1409 |
[11] |
Domingo Tarzia, Carolina Bollo, Claudia Gariboldi. Convergence of simultaneous distributed-boundary parabolic optimal control problems. Evolution Equations & Control Theory, 2020, 9 (4) : 1187-1201. doi: 10.3934/eect.2020045 |
[12] |
Ugur G. Abdulla, Evan Cosgrove, Jonathan Goldfarb. On the Frechet differentiability in optimal control of coefficients in parabolic free boundary problems. Evolution Equations & Control Theory, 2017, 6 (3) : 319-344. doi: 10.3934/eect.2017017 |
[13] |
Dung Le. Strong positivity of continuous supersolutions to parabolic equations with rough boundary data. Discrete & Continuous Dynamical Systems, 2015, 35 (4) : 1521-1530. doi: 10.3934/dcds.2015.35.1521 |
[14] |
Volodymyr O. Kapustyan, Ivan O. Pyshnograiev, Olena A. Kapustian. Quasi-optimal control with a general quadratic criterion in a special norm for systems described by parabolic-hyperbolic equations with non-local boundary conditions. Discrete & Continuous Dynamical Systems - B, 2019, 24 (3) : 1243-1258. doi: 10.3934/dcdsb.2019014 |
[15] |
Ugur G. Abdulla. On the optimal control of the free boundary problems for the second order parabolic equations. I. Well-posedness and convergence of the method of lines. Inverse Problems & Imaging, 2013, 7 (2) : 307-340. doi: 10.3934/ipi.2013.7.307 |
[16] |
Hongwei Lou, Jiongmin Yong. Second-order necessary conditions for optimal control of semilinear elliptic equations with leading term containing controls. Mathematical Control & Related Fields, 2018, 8 (1) : 57-88. doi: 10.3934/mcrf.2018003 |
[17] |
N. Arada, J.-P. Raymond. Time optimal problems with Dirichlet boundary controls. Discrete & Continuous Dynamical Systems, 2003, 9 (6) : 1549-1570. doi: 10.3934/dcds.2003.9.1549 |
[18] |
C. García Vázquez, Francisco Ortegón Gallego. On certain nonlinear parabolic equations with singular diffusion and data in $L^1$. Communications on Pure & Applied Analysis, 2005, 4 (3) : 589-612. doi: 10.3934/cpaa.2005.4.589 |
[19] |
Rosaria Di Nardo. Nonlinear parabolic equations with a lower order term and $L^1$ data. Communications on Pure & Applied Analysis, 2010, 9 (4) : 929-942. doi: 10.3934/cpaa.2010.9.929 |
[20] |
Mostafa Bendahmane, Kenneth Hvistendahl Karlsen, Mazen Saad. Nonlinear anisotropic elliptic and parabolic equations with variable exponents and $L^1$ data. Communications on Pure & Applied Analysis, 2013, 12 (3) : 1201-1220. doi: 10.3934/cpaa.2013.12.1201 |
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