A unique continuation result for the plate equation and an application

Arat, Zehra F. Kabasakal; Khanmamedov, Azer; Simsek, Sema

doi:10.1002/mma.3518

Cited by 4 publications

(2 citation statements)

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“…The theory of attractors for second-order evolution equations was studied and summarized by Chueshov and Lasiecka [1]. Due to the wide applications to the material science, optics, and wave motion, the (second-order) plate PDE (1) (or other forms) has received the attention and research of many scholars; see the case of bounded domains [2][3][4][5][6][7][8][9], the case of unbounded domains [10,11], and the stochastic version [12][13][14].…”

Section: Introductionmentioning

confidence: 99%

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Residually continuous pullback attractors for stochastic discrete plate equations

Han,

Li,

Xia

2024

Math Methods in App Sciences

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For a nonautonomous stochastic discrete plate equation driven by multiplicative noise, we prove the unique existence of a pullback random attractor, which is a family of pullback‐attracting random compact sets parameterized by time and samples. We then establish the residual dense continuity of the pullback random attractor on the time‐sample plane with respect to the Hausdorff metric. Even without the Cantor continuum hypothesis, we show that the set of all points of continuity of the pullback random attractor is an uncountable set with the continuity cardinality. These results explain both nonexplosive and nonimplosive phenomena for the random plate lattice system.

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