BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Sergey Zelik (University of Surrey) DTSTART:20210913T133000Z DTEND:20210913T144500Z DTSTAMP:20260423T052621Z UID:BODS/21 DESCRIPTION:Title: De terministic and random attractors for a wave equation with sign changing d amping\nby Sergey Zelik (University of Surrey) as part of Bremen Onlin e Dynamics Seminar\n\n\nAbstract\nWe discuss the long-time dynamics gener ated\nby weakly damped wave equations in bounded 3D domains where\nthe dam ping coefficient depends explicitly on time and may change sign.\nWe show that in the case when the non-linearity is super-linear\, the\nconsidered equation remains dissipative if the weighted mean value of\nthe dissipatio n rate remains positive and that the conditions of this type\nare not suff icient in the linear case. Two principally different cases will be\nconsi dered. In the case when this mean is uniform (which corresponds\nto determ inistic dissipation rate)\, it will be shown that the considered system\np ossesses smooth uniform attractors as well as non-autonomous exponential\n attractors. In the case where the mean is not uniform (which\ncorresponds to the random dissipation rate\, for instance\, when this dissipation\nrat e is generated by the Bernoulli process)\, the tempered random\nattractor will be constructed. In contrast to the usual situation\, this\nrandom att ractor is expected to have infinite Hausdorff \nand fractal dimensions. T he simplified model example which demonstrates in\nfinite-dimensionality of the random attractor will also be presented.\n LOCATION:https://researchseminars.org/talk/BODS/21/ END:VEVENT END:VCALENDAR