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Russian Mathematical Surveys, 2020, Volume 75, Issue 2, Pages 253–320
DOI: https://doi.org/10.1070/RM9932 (Mi rm9932) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Uniform attractors for measure-driven quintic wave equations

A. K. Savostianova, S. V. Zelikbcd

a Uppsala University, Uppsala, Sweden
b University of Surrey, Guildford, United Kingdom
c School of Mathematics and Statistics, Lanzhou University, Lanzhou, P.R. of China
d Keldysh Institute of Applied Mathematics of Russian Academy of Sciences
English version PDF (950 kB) Citations (8) Russian version article
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DOI: https://doi.org/10.1070/RM9932
Abstract: This is a detailed study of damped quintic wave equations with non-regular and non-autonomous external forces which are measures in time. In the 3D case with periodic boundary conditions, uniform energy-to-Strichartz estimates are established for the solutions, the existence of uniform attractors in a weak or strong topology in the energy phase space is proved, and their additional regularity is studied along with the possibility of representing them as the union of all complete bounded trajectories.
Bibliography: 45 titles.
Keywords: quintic wave equations, vector measures, Strichartz estimates, uniform attractors, smoothness.
Funding agency Grant number
Russian Science Foundation 19-71-30004
Engineering and Physical Sciences Research Council EP/P024920/1
This research was partially supported by the Russian Science Foundation under grant no. 19-71-30004 (§§ 6–8 below) and by the Engineering and Physical Sciences Research Council under grant no. EP/P024920/1.
Received: 19.02.2019
Bibliographic databases:
Document Type: Article
UDC: 517.956.8
MSC: 35B40, 35B45, 35L70
Language: English
Original paper language: Russian
Citation: A. K. Savostianov, S. V. Zelik, “Uniform attractors for measure-driven quintic wave equations”, Russian Math. Surveys, 75:2 (2020), 253–320
Citation in format AMSBIB
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\by A.~K.~Savostianov, S.~V.~Zelik
\paper Uniform attractors for measure-driven quintic wave equations
\jour Russian Math. Surveys
\yr 2020
\vol 75
\issue 2
\pages 253--320
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\crossref{https://doi.org/10.1070/RM9932}
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Linking options:
  • https://www.mathnet.ru/eng/rm9932
  • https://doi.org/10.1070/RM9932
  • https://www.mathnet.ru/eng/rm/v75/i2/p61
    • This publication is cited in the following 8 articles:
    1. Yangmin Xiong, Chunyou Sun, “Kolmogorov ε-entropy of the uniform attractor for a wave equation”, Journal of Differential Equations, 387 (2024), 532  crossref  mathscinet
    2. Q. Chang, D. Li, Ch. Sun, S. V. Zelik, “Deterministic and random attractors for a wave equation with sign changing damping”, Izv. Math., 87:1 (2023), 154–199  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. Russian Math. Surveys, 78:4 (2023), 635–777  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    4. S. Yan, Zh. Tang, Ch. Zhong, “Strong attractors for weakly damped quintic wave equation in bounded domains”, Journal of Mathematical Analysis and Applications, 519:1 (2023), 126752  crossref  mathscinet  zmath
    5. X. Mei, Y. Xiong, Ch. Sun, “Pullback attractor for a weakly damped wave equation with sup-cubic nonlinearity”, Discrete Contin. Dyn. Syst., 41:2 (2021), 569–600  crossref  mathscinet  zmath  isi  scopus
    6. X. Mei, A. Savostianov, Ch. Sun, S. Zelik, “Infinite energy solutions for weakly damped quintic wave equations in R3”, Trans. Amer. Math. Soc., 374:5 (2021), 3093–3129  crossref  mathscinet  zmath  isi  scopus
    7. J. Banaśkiewicz, P. Kalita, “Convergence of non-autonomous attractors for subquintic weakly damped wave equation”, Appl. Math. Optim., 84:S1 (2021), 943–978  crossref  mathscinet  zmath  isi  scopus
    8. A. A. Ilyin, A. A. Laptev, “Magnetic Lieb–Thirring inequality for periodic functions”, Russian Math. Surveys, 75:4 (2020), 779–781  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
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