-
Previous Article
Semi-linear backward stochastic integral partial differential equations driven by a Brownian motion and a Poisson point process
- MCRF Home
- This Issue
-
Next Article
A biographical note and tribute to xunjing li on his 80th birthday
Sparse initial data identification for parabolic PDE and its finite element approximations
1. | Departamento de Matemática Aplicada y Ciencias de la Computación, E.T.S.I. Industriales y de Telecomunicación, Universidad de Cantabria, 39005 Santander, Spain |
2. | Centre for Mathematical Sciences, Technische Universität München, Bolzmannstrasse 3, D-85747 Garching b. München, Germany |
3. | BCAM - Basque Center for Applied Mathematics, Mazarredo, 14, E-48009 Bilbao-Basque Country |
References:
[1] |
Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 13 (1986), 487-535. |
[2] |
Springer-Verlag, New York, Berlin, Heidelberg, 2008, Third edition.
doi: 10.1007/978-0-387-75934-0. |
[3] |
SIAM J. Control Optim., 35 (1997), 1297-1327.
doi: 10.1137/S0363012995283637. |
[4] |
SIAM J. Control Optim., 50 (2012), 1735-1752.
doi: 10.1137/110843216. |
[5] |
SIAM J. Control Optim., 51 (2013), 28-63.
doi: 10.1137/120872395. |
[6] |
SIAM J. Optim., 22 (2012), 795-820.
doi: 10.1137/110834366. |
[7] |
SIAM J. Control Optim., 52 (2014), 339-364.
doi: 10.1137/13092188X. |
[8] |
________, Parabolic control problems in space-time measure spaces,, To appear in ESAIM Control Optim. Calc. Var., (). Google Scholar |
[9] |
SIAM J. Control Optim., 52 (2014), 1010-1033.
doi: 10.1137/130917314. |
[10] |
Systems Control Lett., 62 (2013), 311-318.
doi: 10.1016/j.sysconle.2013.01.001. |
[11] |
ESAIM Control Optim. Calc. Var., 17 (2011), 243-266.
doi: 10.1051/cocv/2010003. |
[12] |
North-Holland-Elsevier, New York, 1976. |
[13] |
Control and optimal design of distributed parameter systems (Minneapolis, MN, 1992), IMA Vol. Math. Appl., Springer, New York, 70 (1995), 73-91.
doi: 10.1007/978-1-4613-8460-1_4. |
[14] |
Advances in Differential Equations, 5 (2000), 465-514. |
[15] |
SIAM J. Control Optim., 52 (2014), 97-119.
doi: 10.1137/110840133. |
[16] |
Adv. Differential Equations, 12 (2007), 1031-1078. |
[17] |
Pitman, Boston-London-Melbourne, 1985. |
[18] |
BIT, 42 (2002), 351-379.
doi: 10.1023/A:1021903109720. |
[19] |
SIAM J. Control Optim., 50 (2012), 943-963.
doi: 10.1137/100815037. |
[20] |
Proc. Amer. Math. Soc., 130 (2002), 1055-1064.
doi: 10.1090/S0002-9939-01-06163-9. |
[21] |
SIAM J. Control Optim., 52 (2014), 3078-3108.
doi: 10.1137/140959055. |
[22] |
SIAM J. Numer. Anal., 51 (2013), 2797-2821.
doi: 10.1137/120885772. |
[23] |
Inverse Probl. and Imaging, 8 (2014), 199-221.
doi: 10.3934/ipi.2014.8.199. |
[24] |
Math. Scand., 8 (1960), 277-286. |
[25] |
SIAM J. Control Optim., 49 (2011), 1961-1997.
doi: 10.1137/100793888. |
[26] |
SIAM J. Control Optim., 51 (2013), 2788-2808.
doi: 10.1137/120889137. |
[27] |
App. Math. Optim., 39 (1999), 143-177.
doi: 10.1007/s002459900102. |
[28] |
McGraw-Hill, London, 1970. Google Scholar |
[29] |
Comm. Pure Appl. Math., 33 (1980), 265-304.
doi: 10.1002/cpa.3160330305. |
[30] |
Comput. Optim. Appl., 44 (2009), 159-181.
doi: 10.1007/s10589-007-9150-9. |
[31] |
Second edition, Spinger-Verlag, Berlin, 2006. |
[32] |
ESAIM Control Optim. Calc. Var., 17 (2011), 858-886.
doi: 10.1051/cocv/2010027. |
show all references
References:
[1] |
Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 13 (1986), 487-535. |
[2] |
Springer-Verlag, New York, Berlin, Heidelberg, 2008, Third edition.
doi: 10.1007/978-0-387-75934-0. |
[3] |
SIAM J. Control Optim., 35 (1997), 1297-1327.
doi: 10.1137/S0363012995283637. |
[4] |
SIAM J. Control Optim., 50 (2012), 1735-1752.
doi: 10.1137/110843216. |
[5] |
SIAM J. Control Optim., 51 (2013), 28-63.
doi: 10.1137/120872395. |
[6] |
SIAM J. Optim., 22 (2012), 795-820.
doi: 10.1137/110834366. |
[7] |
SIAM J. Control Optim., 52 (2014), 339-364.
doi: 10.1137/13092188X. |
[8] |
________, Parabolic control problems in space-time measure spaces,, To appear in ESAIM Control Optim. Calc. Var., (). Google Scholar |
[9] |
SIAM J. Control Optim., 52 (2014), 1010-1033.
doi: 10.1137/130917314. |
[10] |
Systems Control Lett., 62 (2013), 311-318.
doi: 10.1016/j.sysconle.2013.01.001. |
[11] |
ESAIM Control Optim. Calc. Var., 17 (2011), 243-266.
doi: 10.1051/cocv/2010003. |
[12] |
North-Holland-Elsevier, New York, 1976. |
[13] |
Control and optimal design of distributed parameter systems (Minneapolis, MN, 1992), IMA Vol. Math. Appl., Springer, New York, 70 (1995), 73-91.
doi: 10.1007/978-1-4613-8460-1_4. |
[14] |
Advances in Differential Equations, 5 (2000), 465-514. |
[15] |
SIAM J. Control Optim., 52 (2014), 97-119.
doi: 10.1137/110840133. |
[16] |
Adv. Differential Equations, 12 (2007), 1031-1078. |
[17] |
Pitman, Boston-London-Melbourne, 1985. |
[18] |
BIT, 42 (2002), 351-379.
doi: 10.1023/A:1021903109720. |
[19] |
SIAM J. Control Optim., 50 (2012), 943-963.
doi: 10.1137/100815037. |
[20] |
Proc. Amer. Math. Soc., 130 (2002), 1055-1064.
doi: 10.1090/S0002-9939-01-06163-9. |
[21] |
SIAM J. Control Optim., 52 (2014), 3078-3108.
doi: 10.1137/140959055. |
[22] |
SIAM J. Numer. Anal., 51 (2013), 2797-2821.
doi: 10.1137/120885772. |
[23] |
Inverse Probl. and Imaging, 8 (2014), 199-221.
doi: 10.3934/ipi.2014.8.199. |
[24] |
Math. Scand., 8 (1960), 277-286. |
[25] |
SIAM J. Control Optim., 49 (2011), 1961-1997.
doi: 10.1137/100793888. |
[26] |
SIAM J. Control Optim., 51 (2013), 2788-2808.
doi: 10.1137/120889137. |
[27] |
App. Math. Optim., 39 (1999), 143-177.
doi: 10.1007/s002459900102. |
[28] |
McGraw-Hill, London, 1970. Google Scholar |
[29] |
Comm. Pure Appl. Math., 33 (1980), 265-304.
doi: 10.1002/cpa.3160330305. |
[30] |
Comput. Optim. Appl., 44 (2009), 159-181.
doi: 10.1007/s10589-007-9150-9. |
[31] |
Second edition, Spinger-Verlag, Berlin, 2006. |
[32] |
ESAIM Control Optim. Calc. Var., 17 (2011), 858-886.
doi: 10.1051/cocv/2010027. |
[1] |
Guillaume Olive. Boundary approximate controllability of some linear parabolic systems. Evolution Equations & Control Theory, 2014, 3 (1) : 167-189. doi: 10.3934/eect.2014.3.167 |
[2] |
Valentin Keyantuo, Mahamadi Warma. On the interior approximate controllability for fractional wave equations. Discrete & Continuous Dynamical Systems, 2016, 36 (7) : 3719-3739. doi: 10.3934/dcds.2016.36.3719 |
[3] |
Hugo Leiva, Nelson Merentes, José L. Sánchez. Approximate controllability of semilinear reaction diffusion equations. Mathematical Control & Related Fields, 2012, 2 (2) : 171-182. doi: 10.3934/mcrf.2012.2.171 |
[4] |
Vahagn Nersesyan. Approximate controllability of nonlinear parabolic PDEs in arbitrary space dimension. Mathematical Control & Related Fields, 2021, 11 (2) : 237-251. doi: 10.3934/mcrf.2020035 |
[5] |
Farid Ammar Khodja, Cherif Bouzidi, Cédric Dupaix, Lahcen Maniar. Null controllability of retarded parabolic equations. Mathematical Control & Related Fields, 2014, 4 (1) : 1-15. doi: 10.3934/mcrf.2014.4.1 |
[6] |
Lianwen Wang. Approximate controllability and approximate null controllability of semilinear systems. Communications on Pure & Applied Analysis, 2006, 5 (4) : 953-962. doi: 10.3934/cpaa.2006.5.953 |
[7] |
Abdelaziz Bennour, Farid Ammar Khodja, Djamel Teniou. Exact and approximate controllability of coupled one-dimensional hyperbolic equations. Evolution Equations & Control Theory, 2017, 6 (4) : 487-516. doi: 10.3934/eect.2017025 |
[8] |
Pengyu Chen, Xuping Zhang. Approximate controllability of nonlocal problem for non-autonomous stochastic evolution equations. Evolution Equations & Control Theory, 2020 doi: 10.3934/eect.2020076 |
[9] |
Yassine El Gantouh, Said Hadd, Abdelaziz Rhandi. Approximate controllability of network systems. Evolution Equations & Control Theory, 2020 doi: 10.3934/eect.2020091 |
[10] |
Óscar Vega-Amaya, Joaquín López-Borbón. A perturbation approach to a class of discounted approximate value iteration algorithms with borel spaces. Journal of Dynamics & Games, 2016, 3 (3) : 261-278. doi: 10.3934/jdg.2016014 |
[11] |
Franck Boyer, Guillaume Olive. Approximate controllability conditions for some linear 1D parabolic systems with space-dependent coefficients. Mathematical Control & Related Fields, 2014, 4 (3) : 263-287. doi: 10.3934/mcrf.2014.4.263 |
[12] |
Lahcen Maniar, Martin Meyries, Roland Schnaubelt. Null controllability for parabolic equations with dynamic boundary conditions. Evolution Equations & Control Theory, 2017, 6 (3) : 381-407. doi: 10.3934/eect.2017020 |
[13] |
Lydia Ouaili. Minimal time of null controllability of two parabolic equations. Mathematical Control & Related Fields, 2020, 10 (1) : 89-112. doi: 10.3934/mcrf.2019031 |
[14] |
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 |
[15] |
Hans Weinberger. The approximate controllability of a model for mutant selection. Evolution Equations & Control Theory, 2013, 2 (4) : 741-747. doi: 10.3934/eect.2013.2.741 |
[16] |
J. Carmelo Flores, Luz De Teresa. Null controllability of one dimensional degenerate parabolic equations with first order terms. Discrete & Continuous Dynamical Systems - B, 2020, 25 (10) : 3963-3981. doi: 10.3934/dcdsb.2020136 |
[17] |
Morteza Fotouhi, Leila Salimi. Controllability results for a class of one dimensional degenerate/singular parabolic equations. Communications on Pure & Applied Analysis, 2013, 12 (3) : 1415-1430. doi: 10.3934/cpaa.2013.12.1415 |
[18] |
El Mustapha Ait Ben Hassi, Mohamed Fadili, Lahcen Maniar. Controllability of a system of degenerate parabolic equations with non-diagonalizable diffusion matrix. Mathematical Control & Related Fields, 2020, 10 (3) : 623-642. doi: 10.3934/mcrf.2020013 |
[19] |
Enrique Fernández-Cara, Luz de Teresa. Null controllability of a cascade system of parabolic-hyperbolic equations. Discrete & Continuous Dynamical Systems, 2004, 11 (2&3) : 699-714. doi: 10.3934/dcds.2004.11.699 |
[20] |
Fredi Tröltzsch, Daniel Wachsmuth. On the switching behavior of sparse optimal controls for the one-dimensional heat equation. Mathematical Control & Related Fields, 2018, 8 (1) : 135-153. doi: 10.3934/mcrf.2018006 |
2019 Impact Factor: 0.857
Tools
Metrics
Other articles
by authors
[Back to Top]