We consider Cauchy problem for the semilinear plate equation with nonlocal nonlinearity. Under mild conditions on the damping coefficient, we prove that the semigroup generated by this problem possesses a global attractor.2000 Mathematics Subject Classification. 35B41, 35G20, 74K20.

We consider the initial value problem for the semilinear plate equation with nonlocal nonlinearity. We prove the existence of global attractor and then establish the regularity and finite dimensionality of this attractor.Moreover, if (u 0 , u 1 ) ∈ H 4 (R n )×H 2 (R n ), then u is a strong solution from the class C [0, ∞); H 4 (R n ). Therefore, the problem (1.1)-(1.2) generates a strongly continuous semigroup {S (t)} t≥0 in H 2 (R n ) × L 2 (R n ) by the formula (u (t) , u t (t)) = S (t) (u 0 , u 1 ),2000 Mathematics Subject Classification. 35B41, 35G20, 37L30, 74K20.

No abstract

Abstract. In this paper, we prove the unique continuation property for the weak solution of the plate equation with non-smooth coefficients. Then, we apply this result to study the global attractor for the semilinear plate equation with a localized damping.

No abstract