Deterministic and random attractors for a wave equation with sign changing damping
- Авторлар: Chang Q.1, Li D.1, Sun C.1, Zelik S.1,2,3
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Мекемелер:
- Lanzhou University
- University of Surrey
- Keldysh Institute of Applied Mathematics of Russian Academy of Sciences
- Шығарылым: Том 87, № 1 (2023)
- Беттер: 161-210
- Бөлім: Articles
- URL: https://journals.rcsi.science/1607-0046/article/view/142252
- DOI: https://doi.org/10.4213/im9250
- ID: 142252
Дәйексөз келтіру
Аннотация
The paper gives a detailed study of long-time dynamics generated byweakly damped wave equations in bounded 3D domains where the dampingcoefficient depends explicitly on time and may change sign. It is shown thatin the case, where the non-linearity is superlinear, the considered equationremains dissipative if the weighted mean value of the dissipation rateremains positive and that the conditions of this type are not sufficient inthe linear case. Two principally different cases are considered. In thecase when this mean is uniform (which corresponds to deterministicdissipation rate), it is shown that the considered system possesses smoothuniform attractors as well as non-autonomous exponential attractors. In thecase where the mean is not uniform (which corresponds to the randomdissipation rate, for instance, when this dissipation rate is generated bythe Bernoulli process), the tempered random attractor is constructed. Incontrast to the usual situation, this random attractor is expected to haveinfinite Hausdorff and fractal dimensions. The simplified model exampledemonstrating infinite-dimensionality of the random attractor is alsopresented.
Авторлар туралы
Qingquan Chang
Lanzhou University
Email: ddli_dan@yeah.net
Dandan Li
Lanzhou University
Email: ddli_dan@yeah.net
Chunyou Sun
Lanzhou University
Email: ddli_dan@yeah.net
PhD, Professor
Sergey Zelik
Lanzhou University; University of Surrey; Keldysh Institute of Applied Mathematics of Russian Academy of Sciences
Хат алмасуға жауапты Автор.
Email: s.zelik@surrey.ac.uk
Doctor of physico-mathematical sciences, Senior Researcher
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