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Uspekhi Mat. Nauk, 2020, Volume 75, Issue 2(452), Pages 61–132 (Mi umn9932)  

This article is cited in 1 scientific paper (total in 1 paper)

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

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.


DOI: https://doi.org/10.4213/rm9932

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English version:
Russian Mathematical Surveys, 2020, 75:2, 253–320

Bibliographic databases:

UDC: 517.956.8
MSC: 35B40, 35B45, 35L70
Received: 19.02.2019

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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\by A.~K.~Savostianov, S.~V.~Zelik
\paper Uniform attractors for measure-driven quintic wave equations
\jour Uspekhi Mat. Nauk
\yr 2020
\vol 75
\issue 2(452)
\pages 61--132
\mathnet{http://mi.mathnet.ru/umn9932}
\crossref{https://doi.org/10.4213/rm9932}
\transl
\jour Russian Math. Surveys
\yr 2020
\vol 75
\issue 2
\pages 253--320
\crossref{https://doi.org/10.1070/RM9932}
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    This publication is cited in the following articles:
    1. A. A. Ilyin, A. A. Laptev, “Magnetic Lieb–Thirring inequality for periodic functions”, Russian Math. Surveys, 75:4 (2020), 779–781  mathnet  crossref  crossref  isi
  • Успехи математических наук Russian Mathematical Surveys
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