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Existence of strong solutions and global attractors for the coupled suspension bridge equations. (English) Zbl 1176.35036

The authors consider the vibrating beam equation coupled with a vibrating string equation:

u tt +αu xxxx +δ 1 u t +k(u-v) + +f B (u)=h B in[0,L]× + ,v tt -βv xx +δ 2 v t -k(u-v) + +f S (v)=h S in[0,L]× +

with the simply supported boundary conditions at both ends and initial value conditions. For proper k the existence of the strong solution is obtained by the Faedo-Galerkin method. A priori estimates are considered. The authors prove that the solution semigroup defined on the associated product space has a global attractor.

MSC:
35B41Attractors (PDE)
35M31Initial value problems for systems of mixed type
35Q70PDEs in connection with mechanics of particles and systems
47D06One-parameter semigroups and linear evolution equations
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