Issue
ESAIM: COCV
Volume 27, 2021
Special issue in honor of Enrique Zuazua's 60th birthday
Article Number 1
Number of page(s) 35
DOI https://doi.org/10.1051/cocv/2020076
Published online 20 January 2021
  1. H. Antil, R. Khatri and M. Warma, External optimal control of nonlocal PDEs. Inverse Probl. 35 (2019) 084003. [Google Scholar]
  2. H. Antil, R. Nochetto and P. Venegas, Controlling the Kelvin force: basic strategies and applications to magnetic drug targeting. Optim. Eng. 19 (2018) 559–589. [CrossRef] [Google Scholar]
  3. H. Antil, R. Nochetto and P. Venegas, Optimizing the Kelvin force in a moving target subdomain. Math. Models Methods Appl. Sci. 28 (2018) 95–130. [Google Scholar]
  4. H. Antil, D. Verma and M. Warma, External optimal control of fractional parabolic PDEs. ESAIM: COCV 26 (2020). [Google Scholar]
  5. A. Bensoussan, G. Da Prato, M.C. Delfour and S.K. Mitter, Representation and control of infinite dimensional systems. Systems & Control: Foundations & Applications. Birkhäuser, Boston, Inc., Boston, MA, second edition 2007. [CrossRef] [Google Scholar]
  6. U. Biccari, M. Warma and E. Zuazua, Local regularity for fractional heat equations. In Recent advances in PDEs: analysis, numerics and control. Vol. 17 of SEMA SIMAI Springer Ser. Springer, Cham (2018) 233–249. [CrossRef] [Google Scholar]
  7. T. Breiten and L. Pfeiffer, On the turnpike property and the receding-horizon method for linear-quadratic optimal control problems. SIAM J. Control Optim. 58 (2020) 1077–1102. [Google Scholar]
  8. L.A. Caffarelli and L. Silvestre, An extension problem related to the fractional Laplacian. Commun. Partial Differ. Equ. 32 (2007) 1245–1260. [CrossRef] [Google Scholar]
  9. B. Claus and M. Warma, Realization of the fractional Laplacian with nonlocal exterior conditions via forms method. J. Evol. Equ. (2020) 1–35. [Google Scholar]
  10. E. Di Nezza, G. Palatucci and E. Valdinoci, Hitchhiker’s guide to the fractional Sobolev spaces. Bull. Sci. Math. 136 (2012) 521–573. [Google Scholar]
  11. S. Dipierro, X. Ros-Oton and E. Valdinoci, Nonlocal problems with Neumann boundary conditions. Rev. Mat. Iberoam. 33 (2017) 377–416. [CrossRef] [Google Scholar]
  12. R. Dorfman, P.A. Samuelson and R.M. Solow, Linear programming and economic analysis. A Rand Corporation Research Study. McGraw-Hill Book Co., Inc., New York-Toronto-London (1958). [Google Scholar]
  13. Q. Du, M. Gunzburger, R. Lehoucq and K. Zhou, A nonlocal vector calculus, nonlocal volume-constrained problems, and nonlocal balance laws. Math. Models Methods Appl. Sci. 23 (2013) 493–540. [Google Scholar]
  14. C. Esteve, H. Kouhkouh, D. Pighin and E. Zuazua, The turnpike property and the long time-behavior of the Hamilton-Jacobi equation. Preprint arXiv:2006.10430 (2020). [Google Scholar]
  15. T. Faulwasser and D. Bonvin, On the design of economic NMPC based on approximate turnpike properties. In 2015 54th IEEE Conference on Decision and Control (CDC). IEEE (2015) 4964–4970. [CrossRef] [Google Scholar]
  16. C.G. Gal and M. Warma, Nonlocal transmission problems with fractional diffusion and boundary conditions on non-smooth interfaces. Commun. Partial Differ. Equ. 42 (2017) 579–625. [CrossRef] [Google Scholar]
  17. T. Ghosh, M. Salo and G. Uhlmann, The Calderón problem for the fractional Schrödinger equation. Anal. Partial Differ. Equ. 13 (2020) 455–475. [Google Scholar]
  18. P. Grisvard, Elliptic problems in nonsmooth domains, volume 69 of Classics in Applied Mathematics. Reprint of the 1985 original. With a foreword by Susanne C. Brenner. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA 2011. [Google Scholar]
  19. L. Grüne, Economic receding horizon control without terminal constraints. Automatica J. IFAC 49 (2013) 725–734. [CrossRef] [Google Scholar]
  20. L. Grüne, M. Schaller and A. Schiela, Sensitivity analysis of optimal control for a class of parabolic PDEs motivated by model predictive control. SIAM J. Control Optim. 57 (2019) 2753–2774. [Google Scholar]
  21. L. Grüne, M. Schaller and A. Schiela, Exponential sensitivity and turnpike analysis for linear quadratic optimal control of general evolution equations. J. Differ. Equ. 268 (2020) 7311–7341. [Google Scholar]
  22. M. Gugat, E. Trélat and E. Zuazua, Optimal Neumann control for the 1d wave equation: finite horizon, infinite horizon, boundary tracking terms and the turnpike property. Syst. Control Lett. 90 (2016) 61–70. [Google Scholar]
  23. V. Hernández-Santamaría, M. Lazar and E. Zuazua, Greedy optimal control for elliptic problems and its application to turnpike problems. Numer. Math. 141 (2019) 455–493. [Google Scholar]
  24. V. Keyantuo, F. Seoanes and M. Warma, Fractional Gaussian estimates and holomorphy of semigroups. Arch. Math. (Basel) 113 (2019) 629–647. [CrossRef] [Google Scholar]
  25. R. Kress, V. Maz’ya and V. Kozlov, Linear integral equations, volume 82 of Applied Mathematical Sciences. Springer, New York, third edition 1989. [Google Scholar]
  26. G. Lance, E. Trélat and E. Zuazua, Turnpike in optimal shape design. 11th IFAC Symposium on Nonlinear Control Systems NOLCOS 2019. IFAC-PapersOnLine 52 (2019) 496–501. [Google Scholar]
  27. G. Lance, E. Trélat and E. Zuazua, Shape turnpike for linear parabolic PDE models. Syst. Control Lett. 142 (2020) 104733. [Google Scholar]
  28. P.A. Larkin and M. Whalen, Direct, near field acoustic testing. Technical report, SAE technical paper 1999. [Google Scholar]
  29. X.J. Li and J.M. Yong, Optimal control theory for infinite-dimensional systems. Systems & Control: Foundations & Applications. Birkhäuser Boston, Inc., Boston, MA (1995). [Google Scholar]
  30. J.-L. Lions, Optimal control of systems governed by partial differential equations. Translated from the French by S. K. Mitter. Die Grundlehren der mathematischen Wissenschaften, Band 170. Springer-Verlag, New York-Berlin (1971). [Google Scholar]
  31. A. Lübbe, C. Bergemann, H. Riess, F. Schriever, P. Reichardt, K. Possinger, M. Matthias, B. Dörken, F. Herrmann, R. Gürtler, et al., Clinical experiences with magnetic drug targeting: a phase I study with 4’-epidoxorubicin in 14 patients with advanced solid tumors. Cancer Res. 56 (1996) 4686–4693. [Google Scholar]
  32. L.W. McKenzie, Turnpike theorems for a generalized Leontief model. Econometrica (1963) 165–180. [Google Scholar]
  33. E. Niedermeyer and F. da Silva, Electroencephalography: basic principles, clinical applications, and related fields. Lippincott Williams & Wilkins (2005). [Google Scholar]
  34. A. Porretta and E. Zuazua, Long time versus steady state optimal control. SIAM J. Control Optim. 51 (2013) 4242–4273. [Google Scholar]
  35. A. Porretta and E. Zuazua, Remarks on long time versus steady state optimal control. In Mathematical paradigms of climate science, volume 15 of Springer INdAM Ser. Springer, [Cham] (2016) 67–89. [CrossRef] [Google Scholar]
  36. X. Ros-Oton and J. Serra, The extremal solution for the fractional Laplacian. Calc. Var. Partial Differ. Equ. 50 (2014) 723–750. [Google Scholar]
  37. N. Sakamoto, D. Pighin and E. Zuazua, The turnpike property in nonlinear optimal control – a geometric approach. In 2019 IEEE 58th Conference on Decision and Control (CDC) (2019) 2422–2427. [CrossRef] [Google Scholar]
  38. E. Trélat and C. Zhang, Integral and measure-turnpike properties for infinite-dimensional optimal control systems. Math. Control Signals Syst. 30 (2018) 3. [Google Scholar]
  39. E. Trélat, C. Zhang and E. Zuazua, Steady-state and periodic exponential turnpike property for optimal control problems in Hilbert spaces. SIAM J. Control Optim. 56 (2018) 1222–1252. [Google Scholar]
  40. E. Trélat and E. Zuazua, The turnpike property in finite-dimensional nonlinear optimal control. J. Differ. Equ. 258 (2015) 81–114. [Google Scholar]
  41. M. Tucsnak and G. Weiss, Observation and control for operator semigroups. Birkhäuser Advanced Texts: Basler Lehrbücher. [Birkhäuser Advanced Texts: Basel Textbooks]. Birkhäuser Verlag, Basel (2009). [Google Scholar]
  42. M. Tucsnak and G. Weiss, Well-posed systems—the LTI case and beyond. Autom. J. IFAC 50 (2014) 1757–1779. [CrossRef] [Google Scholar]
  43. M. Unsworth, New developments in conventional hydrocarbon exploration with electromagnetic methods. CSEG Recorder 30 (2005) 34–38. [Google Scholar]
  44. M. Warma, The fractional relative capacity and the fractional Laplacian with Neumann and Robin boundary conditions on open sets. Potential Anal. 42 (2015) 499–547. [CrossRef] [Google Scholar]
  45. M. Warma, Approximate controllability from the exterior of space-time fractional diffusive equations. SIAM J. Control Optim. 57 (2019) 2037–2063. [Google Scholar]
  46. M. Warma and S. Zamorano, Null controllability from the exterior of a one-dimensional nonlocal heat equation. Control Cybern. 48 (2019) 417–438. [Google Scholar]
  47. C. Weiss, B. Waanders and H. Antil, Fractional operators applied to geophysical electromagnetics. Geophys. J. Int. 220 (2020) 1242–1259. [Google Scholar]
  48. R. Williams, I. Karacan and C. Hursch, Electroencephalography (EEG) of human sleep: clinical applications. John Wiley & Sons (1974). [Google Scholar]
  49. S. Zamorano, Turnpike property for two-dimensional Navier-Stokes equations. J. Math. Fluid Mech. 20 (2018) 869–888. [Google Scholar]
  50. A.J. Zaslavski, Turnpike properties in the calculus of variations and optimal control. Volume 80 of Nonconvex Optimization and its Applications. Springer, New York (2006). [Google Scholar]
  51. A.J. Zaslavski, Turnpike conditions in infinite dimensional optimal control. Vol. 148 of Springer Optimization and Its Applications. Springer, Cham (2019). [CrossRef] [Google Scholar]
  52. E. Zeidler, Nonlinear functional analysis and its applications. II/A. Linear monotone operators, Translated from the German by the author and Leo F. Boron. Springer-Verlag, New York (1990). [Google Scholar]
  53. E. Zuazua, Large time control and turnpike properties for wave equations. Annu. Rev. Control 44 (2017) 199–210. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.