Deterministic and random attractors for a wave equation with sign changing damping
Sergey Zelik (University of Surrey)
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
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Organizer: | Researchers from University of Bremen and Jacobs University Bremen |
Curator: | Anke Pohl* |
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