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Department of Mathematical Sciences

Research Seminar Series

Applied Mathematics Seminars: Smooth uniform attractors for a measure driven quintic damped wave equation on 3D torus

Presented by Anton Savostianov, Durham University

5 May 2017 14:30 in CM219

In this talk I would like to present new results concerning the existence of smooth uniform attractors for nonautonomous damped wave equation with nonlinearities of quintic growth. It is well known that to prove even wellposedness of the wave equation in 3D with fast enough growing nonlinearities the only energy estimate is not enough and some extra estimates, known as Strichartz estimates, are required. To the best of our knowledge, previously these type of estimates, in the critical quintic case, were known only for the autonomous equation. We prove that Strichartz type estimates remain valid for the quintic wave equation with nonatunomous forcing. Furthermore, it appears that the forcing can be given by a vector-valued measure with bounded total variation. Based on these estimates we introduce several classes of "nice" external forces for which we show that the quintic damped wave equation possesses smooth uniform attractors. This is joint work with Sergey Zelik.

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This seminar series is the continuation of the Numerical Analysis Seminar series that ran until August 2016. This change of name reflects the broader interests of the Applied Mathematics group (note that the Mathematical and Theoretical Particle Physics group also has a seminar series).

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