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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: $$\align u_{tt}+ \alpha u_{xxxx}+\delta_1 u_t+ k(u- v)^++ f_B(u)= h_B\quad &\text{in }[0,L]\times \bbfR^+,\\ v_{tt}- \beta v_{xx}+ \delta_2 v_t- k(u- v)^++ f_S(v)= h_S\quad &\text{in }[0,L]\times \bbfR^+\endalign$$ 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.

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
Full Text: DOI
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