Issue
ESAIM: COCV
Volume 27, 2021
Special issue in the honor of Enrique Zuazua's 60th birthday
Article Number 57
Number of page(s) 23
DOI https://doi.org/10.1051/cocv/2021053
Published online 04 June 2021
  1. A. Balogh, D.S. Gilliam and V.I. Shubov, Some recent results on feedback regularization of Navier-Stokes equations., Proceedings of the 36th Conference on Decision & Control, San Diego, California USA (1997) 2231–2236. [Google Scholar]
  2. T. Cazenave and A. Haraux, An Introduction to Semilinear Evolution Equations. Oxford Lecture Series in Mathematics and its Applications, Oxford University Press (1980). [Google Scholar]
  3. S. Dashkovskiy and A. Mironchenko, Input-to-state stability of infinite-dimensional control systems. Math. Control Signals Syst. 25 (2013) 1–35. [Google Scholar]
  4. A. Friedman, Partial Differential Equations of Parabolic Type, Dover (2008). [Google Scholar]
  5. M. Gunzburger, E. Lee, Y. Saka, C. Trenchea and X. Wang, Analysis of nonlinear spectral Eddy-viscosity models of turbulence. J. Sci. Comput. 45 (2010) 294–332. [Google Scholar]
  6. F. Hamba, Nonlocal expression for scalar flux in turbulent shear flow. Phys. Fluids 16 (2004) 1493–1508. [Google Scholar]
  7. B. Jacob, R. Nabiullin, J.R. Partington and F.L. Schwenninger, Infinite-dimensional input-to-state stability and Orlicz spaces. SIAM J. Control Optim. 56 (2018) 868–889. [Google Scholar]
  8. B. Jacob, F.L. Schwenninger and H. Zwart, On continuity of solutions for parabolic control systems and input-to-state stability. J. Differ. Equ. 266 (2019) 6284–6306. [Google Scholar]
  9. B. Jacob, A. Mironchenko, J.R. Partington and F. Wirth, Non-coercive Lyapunov functions for input-to-state stability of infinite-dimensional systems. SIAM J. Control Optim. 58 (2020) 2952–2978. [Google Scholar]
  10. F. John, Partial Differential Equations, 4th Edition, Springer-Verlag, New York (1982). [Google Scholar]
  11. I. Karafyllis and Z.-P. Jiang, Stability and Stabilization of Nonlinear Systems. Springer-Verlag, London (Series: Communications and Control Engineering) (2011). [Google Scholar]
  12. I. Karafyllis and M. Krstic, ISS in different norms for 1-D parabolic PDEs with boundary disturbances. SIAM J. Control Optim. 55 (2017) 1716–1751. [Google Scholar]
  13. I. Karafyllis and M. Krstic, Sampled-data boundary feedback control of 1-D parabolic PDEs. Automatica 87 (2018) 226–237. [Google Scholar]
  14. I. Karafyllis and M. Krstic, Decay estimates for 1-D parabolic PDEs with boundary disturbances. ESAIM: COCV 24 (2018) 1511–1540. [EDP Sciences] [Google Scholar]
  15. I. Karafyllis and M. Krstic, Small-gain-based boundary feedback design for global exponential stabilization of 1-D semilinear parabolicPDEs. SIAM J. Control Optim. 57 (2019) 2016–2036. [Google Scholar]
  16. I. Karafyllis and M. Krstic, Input-to-State Stability for PDEs. Springer-Verlag, London (Series: Communications and Control Engineering) (2019). [Google Scholar]
  17. I. Karafyllis, T. Ahmed-Ali and F. Giri, Sampled-data observers for 1-D parabolic PDEs with non-local outputs. Syst. Control Lett. 133 (2019) 104553. [Google Scholar]
  18. O.A. Ladyzhenskaya, V.A. Solonnikov and N.N. Ural’ceva, Linear and Quasilinear Equations of Parabolic Type. Trans. AMS 23 (1968). [Google Scholar]
  19. O.A. Ladyzhenskaya, New equations for the description of the motions of viscous incompressible fluids, and global solvability for their boundary value problems. Bound. Value Probl. Math. Phys. Part 5, Trudy Matematicheskogo Instituta imeni V.A. Steklova 102 (1967) 85–104 and Proc. Steklov Inst. Math. 102 (1967) 95–118. [Google Scholar]
  20. A. Mironchenko and F. Wirth, Characterizations of input-to-state stability for infinite-dimensional systems. IEEE Trans. Autom. Control 63 (2018) 1602–1617. [Google Scholar]
  21. A. Mironchenko, I. Karafyllis and M. Krstic, Monotonicity methods for input-to-state stability of nonlinear parabolic PDEs with boundary disturbances. SIAM J. Control Optim. 57 (2019) 510–532. [Google Scholar]
  22. A. Mironchenko and C. Prieur, Input-to-state stability of infinite-dimensional systems: recent results and open questions. SIAM Rev. 62 (2020) 529–614. [Google Scholar]
  23. M.H. Protter and H.F. Weinberger, Maximum Principles in Differential Equations. Springer-Verlag, New York (1984). [Google Scholar]
  24. G.A. Slack, Nonmetallic crystals with high thermal conductivity. J. Phys. Chem. Solids 34 (1973) 321–335. [Google Scholar]
  25. J. Smoller, Shock Waves and Reaction-Diffusion Equations, 2nd edition, Springer-Verlag, New York (1994). [Google Scholar]
  26. A. Tanwani, C. Prieur and S. Tarbouriech, Disturbance-to-state stabilization and quantized control for linear hyperbolic systems. arXiv:1703.00302. [Google Scholar]
  27. R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, 2nd edition, Springer (1997). [Google Scholar]
  28. J. Zheng and G. Zhu, Input-to-state stability with respect to boundary disturbances for a class of semi-linear parabolic equations. Automatica 97 (2018) 271–277. [Google Scholar]
  29. J. Zheng and G. Zhu, A De Giorgi iteration-based approach for the establishment of ISS properties for Burgers’ equation with boundary and in-domain disturbances. IEEE Trans. Autom. Control 64 (2019) 3476–3483. [Google Scholar]
  30. J. Zheng and G. Zhu, A weak maximum principle-based approach for input-to-state stability analysis of nonlinear parabolic PDEs with boundary disturbances. Math. Control Signals Syst. 32 (2020) 157–176. [Google Scholar]
  31. J. Zheng and G. Zhu, ISS-like estimates for nonlinear parabolic PDEs with variable coefficients on higher dimensional domains. Syst. Control Lett. 146 (2020) 104808. [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.