Finite-dimensional attracting invariant manifolds for damped semilinear wave equations. (English) Zbl 0642.35061

Mora, X.

Contributions to nonlinear partial differential equations, Vol. II, Proc. 2nd Franco-Span. Colloq., Paris 1985, Pitman Res. Notes Math. Ser. 155, 172-183 (1987).

[For the entire collection see Zbl 0614.00011.]
It is shown that, when the damping is sufficiently large, the dynamical system generated by certain semilinear damped wave equations has the property that its global attractor is contained in a finite-dimensional local invariant manifold of class C 1.

Reviewer: X.Mora

MSC:

35L70	Second-order nonlinear hyperbolic equations
37-XX	Dynamical systems and ergodic theory
35B40	Asymptotic behavior of solutions to PDEs

Keywords:

inertial manifolds; damping; dynamical system; semilinear; wave equations; global attractor; local invariant manifold