Open Access
Issue
ESAIM: COCV
Volume 27, 2021
Article Number 59
Number of page(s) 24
DOI https://doi.org/10.1051/cocv/2021047
Published online 07 June 2021
  1. P. Acquistapace and B. Terreni, Infinite-horizon linear-quadratic regulator problems for nonautonomous parabolic systems with boundary control. SIAM J. Control Optim. 34 (1996) 1–30. [Google Scholar]
  2. N. Anantharaman and M. Léautaud, Sharp polynomial decay rates for the damped wave equation on the torus. Anal. PDE 7 (2014) 159–214. (With an appendix by Stéphane Nonnenmacher). [Google Scholar]
  3. E.R. Aragão-Costa, T. Caraballo, A.N. Carvalho and J.A. Langa, Non-autonomous Morse decomposition and Lyapunov functions for dynamically gradient processes. Trans. Am. Math. Soc. 365 (2013) 5277–5312. [Google Scholar]
  4. M. Balti and R. May, Asymptotic for the perturbed heavy ball system with vanishing damping term. Evol. Equ. Control Theory 6 (2017) 177–186. [Google Scholar]
  5. C.J.K. Batty, A. Borichev and Y. Tomilov, Lp-tauberian theorems and Lp-rates for energy decay. J. Functional Anal. 270 (2016) 1153–1201. [Google Scholar]
  6. N. Burq and R. Joly, Exponential decay for the damped wave equation in unbounded domains. Commun. Contemp. Math. 18 (2016) 1650012. [Google Scholar]
  7. A. Cabot and P. Frankel, Asymptotics for some semilinear hyperbolic equations with non-autonomous damping. J. Differ. Equ. 252 (2012) 294–322. [Google Scholar]
  8. A.N. Carvalho and J.A. Langa, The existence and continuity of stable and unstable manifolds for semilinear problems under non-autonomous perturbation in Banach spaces. J. Differ. Equ. 233 (2007) 622–653. [Google Scholar]
  9. A.N. Carvalho, J.A. Langa and J.C. Robinson, Attractors for infinite-dimensional non-autonomous dynamical systems. In vol. 182 of Applied Mathematical Sciences. Springer, New York (2013). [Google Scholar]
  10. M. Daoulatli, Rates of decay for the wave systems with time-dependent damping. Discrete Contin. Dyn. Syst. 31 (2011) 407–443. [Google Scholar]
  11. G. Dore, A. Favini, R. Labbas and K. Lemrabet, An abstract transmission problem in a thin layer, I: Sharp estimates. J. Functional Anal. 261 (2011) 1865–1922. [Google Scholar]
  12. H.O. Fattorini, The Cauchy Problem. With a Foreword by Felix E. Browder, reprint of the 1983 original, In Vol. 18 of Encyclopedia Mathematics and its Applications. Cambridge University Press, Cambridge (2008). [Google Scholar]
  13. A. Favini, Degenerate and singular evolution equations in Banach space. Math. Ann. 273 (1985) 17–44. [Google Scholar]
  14. A. Favini, C.G. Gal, G.R. Goldstein, J.A. Goldstein and S. Romanelli, The non-autonomous wave equation with general Wentzell boundary conditions. Proc. Roy. Soc. Edinburgh Sect. A 135 (2005) 317–329. [Google Scholar]
  15. A. Favini and G. Marinoschi, Degenerate Nonlinear Diffusion Equations. Vol. 2049 of Lecture Notes in Mathematics. Springer, Heidelberg (2012). [Google Scholar]
  16. J.A. Goldstein, Time dependent hyperbolic equations. J. Functional Anal. 4 (1969) 31–49. [Google Scholar]
  17. J.A. Goldstein, Semigroups of Linear Operators and Applications. Oxford Mathematical Monographs, Oxford University Press, New York (1985). [Google Scholar]
  18. M. Ghisi, M. Gobbino and A. Haraux, Optimal decay estimates for the general solution to a class of semil-linear dissipative hyperbolic eqiations. J. Eur. Math. Soc. (JEMS) 18 (2016) 1961–1982. [Google Scholar]
  19. M. Ghisi, M. Gobbino and A. Haraux, Finding the exact decay rate of all solutions to some second order evolution equations with dissipation. J. Functional Anal. 271 (2016) 2359–2395. [Google Scholar]
  20. A. Haraux, Slow and fast decay of solutions to some second order evolution equations. J. Anal. Math. 95 (2005) 297–321. [Google Scholar]
  21. A. Haraux, Decay rate of the range component of solutions to some semilinear evolution equations. NoDEA Nonlinear Differ. Equ. Appl. 13 (2006) 435–445. [Google Scholar]
  22. K.P. Jin, J. Liang and T.J. Xiao, Coupled second order evolution equations with fading memory: Optimal energy decay rate. J. Differ. Equ. 257 (2014) 1501–1528. [Google Scholar]
  23. K.P. Jin, J. Liang and T.J. Xiao, Uniform stability of semilinear wave equations with arbitrary local memory effects versus frictional dampings. J. Differ. Equ. 266 (2019) 7230–7263. [Google Scholar]
  24. P.E. Kloeden and M. Rasmussen, Vol. 176 of Nonautonomous Dynamical Systems. Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI (2011). [Google Scholar]
  25. J.A. Langa, J.C. Robinson, A. Suárez and A. Vidal-López, The stability of attractors for non-autonomous perturbations of gradient-like systems. J. Differ. Equ. 234 (2007) 607–625. [Google Scholar]
  26. J. Liang, R. Nagel and T.J. Xiao, Approximation theorems for the propagators of higher order abstract Cauchy problems. Trans. Am. Math. Soc. 360 (2008) 1723–1739. [Google Scholar]
  27. J.L. Lions, Controlabilité exacte, perturbations et stabilisation de systèmes distribués 1, Masson, Paris (1988). [Google Scholar]
  28. J.R. Luo and T.J. Xiao, Decay rates for second order evolution equations in Hilbert spaces with nonlinear time-dependent damping. Evol. Equ. Control Theory 9 (2020) 359–373. [Google Scholar]
  29. P. Martinez, A new method to obtain decay rate estimates for dissipative systems. ESAIM: COCV 4 (1999) 419–444. [CrossRef] [EDP Sciences] [Google Scholar]
  30. P. Martinez, Precise decay rate estimates for time-dependent dissipative systems. Israel J. Math. 119 (2000) 291–324. [Google Scholar]
  31. R. May, Long time behavior for a semilinear hyperbolic equation with asymptotically vanishing damping term and convex potential. J. Math. Anal. Appl. 430 (2015) 410–416. [Google Scholar]
  32. M. Nakao, On the time decay of solutions of the wave equation with a local time-dependent nonlinear dissipation. Adv. Math. Sci. Appl. 7 (1997) 317–331. [Google Scholar]
  33. T.J. Xiaoand J. Liang, Coupled second order semilinear evolution equations indirectly damped via memory effects. J. Differ. Equ. 254 (2013) 2128–2157. [Google Scholar]
  34. T.J. Xiao and J. Liang, Nonautonomous semilinear second order evolution equations with generalized Wentzell boundary conditions. J. Differ. Equ. 252 (2012) 3953–3971. [Google Scholar]
  35. T.J. Xiaoand J. Liang, Vol. 1701 of The Cauchy Problem for Higher Order Abstract Differential Equations. Lecture Notes in Mathematics. Springer, Berlin (1998). [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.