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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)
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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
Russian version:
Uspekhi Matematicheskikh Nauk, 2020, Volume 75, Issue 2(452), Pages 61–132
DOI: https://doi.org/10.4213/rm9932
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”, Uspekhi Mat. Nauk, 75:2(452) (2020), 61–132; Russian Math. Surveys, 75:2 (2020), 253–320
Citation in format AMSBIB
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    • This publication is cited in the following 8 articles:
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    Russian version PDF:84
    English version PDF:28
    References:67
    First page:37
     
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