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Global attractor for a nonlinear plate equation with supported boundary conditions. (English) Zbl 1181.35028

Summary: We consider a two-dimensional nonlinear equation
\[ \rho w-{tt}_ D\Delta^2w+ \varepsilon\mu w_t- \bigg(N_1+\frac T2 \int_\Omega w_x^2\,dx\,dy\bigg)w_{xx}- \bigg(N_2+ \frac T2 \int_\Omega w_y^2\,dx\,dy\bigg) w_{yy}=0, \]
which arises from the model of the viscoelastic thin rectangular plate with four edges supported. By virtue of Galerkin method combined with the priori estimates, we prove the existence and uniqueness of the global solution under initial-boundary data for the above equation. Especially the existence of the bounded absorbing set in space \(E\) and the existence of the global attractor of system is also obtained.

MSC:

35B41 Attractors
74K20 Plates
35L76 Higher-order semilinear hyperbolic equations
35L35 Initial-boundary value problems for higher-order hyperbolic equations
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