Deterministic and random attractors for a wave equation with sign changing damping

Sergey Zelik (University of Surrey)

13-Sep-2021, 13:30-14:45 (3 years ago)

Abstract: We discuss the long-time dynamics generated by weakly damped wave equations in bounded 3D domains where the damping coefficient depends explicitly on time and may change sign. We show that in the case when the non-linearity is super-linear, the considered equation remains dissipative if the weighted mean value of the dissipation rate remains positive and that the conditions of this type are not sufficient in the linear case. Two principally different cases will be considered. In the case when this mean is uniform (which corresponds to deterministic dissipation rate), it will be shown that the considered system possesses smooth uniform attractors as well as non-autonomous exponential attractors. In the case where the mean is not uniform (which corresponds to the random dissipation rate, for instance, when this dissipation rate is generated by the Bernoulli process), the tempered random attractor will be constructed. In contrast to the usual situation, this random attractor is expected to have infinite Hausdorff and fractal dimensions. The simplified model example which demonstrates in finite-dimensionality of the random attractor will also be presented.

dynamical systems

Audience: researchers in the topic


Bremen Online Dynamics Seminar

Series comments: Talks are approx. 55 min plus discussion. Talks are not recorded.

The meeting links are announced via the seminar mailing list, a few days before the talks. To subscribe please send an email with subject "subscribe" (without the ") to bods-request@mailman.zfn.uni-bremen.de or visit the webpage

mailman.zfn.uni-bremen.de/cgi-bin/mailman/listinfo/bods

This mailing list is used only for the purpose of the announcements. No spam! You can unsubscribe at any time following the instructions in the emails or on the webpage above.

Organizer: Researchers from University of Bremen and Jacobs University Bremen
Curator: Anke Pohl*
*contact for this listing

Export talk to