Attractors for a plate equation with nonlocal nonlinearities | Zendy

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Attractors for a plate equation with nonlocal nonlinearities

Author(s) -

Narciso Vando

Publication year - 2017

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.4275

Subject(s) - attractor , mathematics , bounded function , open set , boundary (topology) , stability (learning theory) , class (philosophy) , mathematical analysis , nonlinear system , limit (mathematics) , limit set , boundary value problem , limit cycle , set (abstract data type) , pure mathematics , physics , quantum mechanics , machine learning , artificial intelligence , computer science , programming language

This paper contains results on well‐posedness, stability, and long‐time behavior of solutions to a class of plate models subject to damping and source terms given by the product of two nonlinear components [EQUATION1] where Ω is a bounded open set of R n with smooth boundary, γ , ρ ⩾0 andl 1 ( u ) , l 2 ( u ) are nonlocal functions. The main result states that the dynamical system { S ( t )} t ⩾0 associated with this problem has a compact global attractor. In addition, in the limit case γ = 0, it is also shown that { S ( t )} t ⩾0 has a finite dimensional global attractor by using an approach on quasi‐stability because of Chueshov–Lasiecka (2010). Copyright © 2017 John Wiley & Sons, Ltd.

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