[1]
|
Troltzsch, F. (2010) Optimal Control of Partial Differential Equations: Theory, Methods, and
Applications. American Mathematical Society, Providence, RI.
|
[2]
|
Stadler, G. (2009) Elliptic Optimal Control Problems with L1-Control Cost and Applications
for the Placement of Control Devices. Computational Optimization and Applications, 44, 159-
181. https://doi.org/10.1007/s10589-007-9150-9
|
[3]
|
Wachsmuth, G. and Wachsmuth, D. (2011) Convergence and Regularization Results for Optimal
Control Problems with Sparsity Functional. ESAIM: Control, Optimisation and Calculus
of Variations, 17, 858-886. https://doi.org/10.1051/cocv/2010027
|
[4]
|
Casas, E., Clason, C. and Kunisch, K. (2012) Approximation of Elliptic Control Problems
in Measure Spaces with Sparse Solutions. SIAM Journal on Control and Optimization, 50,
1735-1752. https://doi.org/10.1137/110843216
|
[5]
|
Casas, E. and Kunisch, K. (2014) Optimal Control of Semilinear Elliptic Equations in Measure
Spaces. SIAM Journal on Control and Optimization, 52, 339-364.
https://doi.org/10.1137/13092188X
|
[6]
|
Casas, E., Herzog, R. and Wachsmuth, G. (2012) Optimality Conditions and Error Analysis of
Semilinear Elliptic Control Problems with L1 Cost Functional. SIAM Journal on Optimization,
22, 795-820. https://doi.org/10.1137/110834366
|
[7]
|
Casas, E. and Kunisch, K. (2016) Parabolic Control Problems in Space-Time Measure Spaces.
ESAIM: Control, Optimisation and Calculus of Variations, 22, 355-370.
https://doi.org/10.1051/cocv/2015008
|
[8]
|
Casas, E., Clason, C. and Kunisch, K. (2013) Parabolic Control Problems in Measure Spaces
with Sparse Solutions. SIAM Journal on Control and Optimization, 51, 28-63.
https://doi.org/10.1137/120872395
|
[9]
|
Kunisch, K., Pieper, K. and Vexler, B. (2014) Measure Valued Directional Sparsity for Parabolic
Optimal Control Problems. SIAM Journal on Control and Optimization, 52, 3078-3108.
https://doi.org/10.1137/140959055
|
[10]
|
Casas, E., Herzog, R. and Wachsmuth, G. (2017) Analysis of Spatio-Temporally Sparse Optimal
Control Problems of Semilinear Parabolic Equations. ESAIM: Control, Optimisation and
Calculus of Variations, 23, 263-295. https://doi.org/10.1051/cocv/2015048
|
[11]
|
Mateos, M. (2021) Sparse Dirichlet Optimal Control Problems. Computational Optimization
and Applications, 80, 271-300. https://doi.org/10.1007/s10589-021-00290-7
|
[12]
|
Lions, J.L. (1971) Optimal Control of Systems Governed by Partial Differential Equations.
Springer, Berlin.
|
[13]
|
Lions, J.L. and Magenes, E. (1972) Non-Homogeneous Boundary Value Problems and Applications.
Volume II. Springer, Berlin, Heidelberg.
|
[14]
|
Gong, W., Hinze, M. and Zhou, Z. (2016) Finite Element Method and a Priori Error Estimates
for Dirichlet Boundary Control Problems Governed by Parabolic PDEs. Journal of Scientific
Computing, 66, 941-967. https://doi.org/10.1007/s10915-015-0051-2
|
[15]
|
Evans, L.C. (2022) Partial Differential Equations. American Mathematical Society, Providence,
RI.
|
[16]
|
Berggren, M. (2004) Approximations of Very Weak Solutions to Boundary-Value Problems.
SIAM Journal on Numerical Analysis, 42, 860-877.
https://doi.org/10.1137/S0036142903382048
|
[17]
|
Kunisch, K. and Vexler, B. (2007) Constrained Dirichlet Boundary Control in L2 for a Class
of Evolution Equations. SIAM Journal on Control and Optimization, 46, 1726-1753.
https://doi.org/10.1137/060670110
|
[18]
|
Casas, E., Mateos, M. and Raymond, J.P. (2009) Penalization of Dirichlet Optimal Control
Problems. ESAIM: Control, Optimisation and Calculus of Variations, 15, 782-809.
https://doi.org/10.1051/cocv:2008049
|
[19]
|
Ekeland, I. and Temam, R. (1999) Convex Analysis and Variational Problems. Society for
Industrial and Applied Mathematics, Philadelphia, PA.
https://doi.org/10.1137/1.9781611971088
|
[20]
|
Casas, E. (2012) Second Order Analysis for Bang-Bang Control Problems of PDEs. SIAM
Journal on Control and Optimization, 50, 2355-2372. https://doi.org/10.1137/120862892
|
[21]
|
Edwards, R.E. (2012) Functional Analysis: Theory and Applications. Dover, Mineola, NY.
|
[22]
|
Herzog, R., Obermeier, J. and Wachsmuth, G. (2015) Annular and Sectorial Sparsity in Optimal
Control of Elliptic Equations. Computational Optimization and Applications, 62, 157-180.
https://doi.org/10.1007/s10589-014-9721-5
|
[23]
|
Gong, W. and Li, B. (2020) Improved Error Estimates for Semidiscrete Finite Element Solutions
of Parabolic Dirichlet Boundary Control Problems. IMA Journal of Numerical Analysis,
40, 2898-2939. https://doi.org/10.1093/imanum/drz029
|