Issue
ESAIM: COCV
Volume 27, 2021
Special issue in the honor of Enrique Zuazua's 60th birthday
Article Number 84
Number of page(s) 62
DOI https://doi.org/10.1051/cocv/2021067
Published online 27 July 2021
  1. F. Alabau-Boussouira, On some recent advances on stabilization for hyperbolic equations, in Control of partial differential equations. Vol. 2048 of Lecture Notes in Math. Springer, Heidelberg (2012) 1–100. [Google Scholar]
  2. D. Amadori, F.A.-Z. Aqel and E.D. Santo, Decay of approximate solutions for the damped semilinear wave equation on a bounded 1d domain. J. Math. Pures Appl. 132 (2019) 166–206. [Google Scholar]
  3. S. Amin, F.M. Hante and A.M. Bayen, Exponential stability of switched linear hyperbolic initial-boundary value problems. IEEE Trans. Automat. Control 57 (2012) 291–301. [Google Scholar]
  4. J.-P. Aubin and A. Cellina, Differential inclusions. Set-valued maps and viability theory. Vol. 264 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, Berlin (1984). [Google Scholar]
  5. G. Bastin and J.-M. Coron, Vol. 88 of Stability and boundary stabilization of 1-d hyperbolic systems. Springer (2016). [Google Scholar]
  6. D.P. Bertsekas and S.E. Shreve, Stochastic optimal control: The discrete time case. Vol. 139 of Mathematics in Science and Engineering. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London (1978). [Google Scholar]
  7. Y. Chitour, S. Marx and C. Prieur, Lp-asymptotic stabilityanalysis of a 1d wave equation with a nonlinear damping. J. Differ. Equ. 269 (2020) 8107–8131. [Google Scholar]
  8. Y. Chitour, G. Mazanti and M. Sigalotti, Stability of non-autonomous difference equations with applications to transport and wave propagation on networks. Netw. Heterog. Media 11 (2016) 563–601. [Google Scholar]
  9. D.L. Cohn, Measure theory. Birkhäuser Advanced Texts: Basler Lehrbücher. [Birkhäuser Advanced Texts: Basel Textbooks]. Birkhäuser/Springer, New York, second edition (2013). [Google Scholar]
  10. L.C. Evans, Partial differential equations. Vol. 19 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, second edition (2010). [Google Scholar]
  11. A.F. Filippov, Differential equations with discontinuous righthand sides. Vol. 18 of Mathematics and its Applications (Soviet Series). Translated from the Russian. Kluwer Academic Publishers Group, Dordrecht (1988). [Google Scholar]
  12. M. Gugat and M. Sigalotti, Stars of vibrating strings: switching boundary feedback stabilization. Netw. Heterog. Media 5 (2010) 299–314. [Google Scholar]
  13. I. Haidar, Y. Chitour, P. Mason and M. Sigalotti, Lyapunov characterization of uniform exponential stability for nonlinear infinite-dimensional systems. Preprint arXiv:2002.06822 (2020). [Google Scholar]
  14. A. Haraux, Lp estimates of solutions to some non-linear wave equations in one space dimension. Int. J. Math. Model. Numer. Optim. 1 (2009) 146–152. [Google Scholar]
  15. Z.-P. Jiang and Y. Wang, Input-to-state stability for discrete-time nonlinear systems. Automatica J. IFAC 37 (2001) 857–869. [Google Scholar]
  16. P.-O. Lamare, A. Girard and C. Prieur, Switching rules for stabilization of linear systems of conservation laws. SIAM J. Control Optim. 53 (2015) 1599–1624. [Google Scholar]
  17. I. Lasiecka and D. Tataru, Uniform boundary stabilization of semilinear wave equations with nonlinear boundary damping. Differ. Integr. Equ. 6 (1993) 507–533. [Google Scholar]
  18. D. Liberzon, Switching in systems and control. Systems & Control: Foundations & Applications. Birkhäuser Boston, Inc., Boston, MA (2003). [Google Scholar]
  19. W.-J. Liu and E. Zuazua, Decay rates for dissipative wave equations. Ricerche Mat. 48 (1999) 61–75. Papers in memory of Ennio De Giorgi. [Google Scholar]
  20. P. Martinez, A new method to obtain decay rate estimates for dissipative systems. ESAIM: COCV 4 (1999) 419–444. [CrossRef] [EDP Sciences] [Google Scholar]
  21. 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]
  22. A. Mironchenko and F. Wirth, Characterizations of input-to-state stability for infinite-dimensional systems. IEEE Trans. Automat. Control 63 (2018) 1602–1617. [Google Scholar]
  23. T. Nishiura, Absolute measurable spaces. Vol. 120 of Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge (2008). [Google Scholar]
  24. J. Peral, Lp estimates for the wave equation. J. Funct. Anal. 36 (1980) 114–145. [Google Scholar]
  25. M. Pierre and J. Vancostenoble, Strong decay for one-dimensional wave equations with nonmonotone boundary damping. Control Cybern. 29 (2000) 473–484. [Google Scholar]
  26. J. Vancostenoble and P. Martinez, Optimality of energy estimates for the wave equation with nonlinear boundary velocity feedbacks. SIAM J. Control Optim. 39 (2000) 776–797. [Google Scholar]
  27. C.-Z. Xu and G.Q. Xu, Saturated boundary feedback stabilization of a linear wave equation. SIAM J. Control Optim. 57 (2019) 290–309. [Google Scholar]
  28. E. Zuazua, Uniform stabilization of the wave equation by nonlinear boundary feedback. SIAM J. Control Optim. 28 (1990) 466–477. [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.