This article is cited in 11 papers

Uniform attractors for measure-driven quintic wave equations

A. K. Savostianov^a, S. V. Zelik<sup>bcd

a</sup> 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.

UDC: 517.956.8

MSC: 35B40, 35B45, 35L70

Received: 19.02.2019

DOI: 10.4213/rm9932

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

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