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Long-time dynamics for a class of extensible beams with nonlocal nonlinear damping. (English) Zbl 1366.35185

Summary: In this paper we consider new results on well-posedness and long-time dynamics for a class of extensible beam/plate models whose dissipative effect is given by the product of two nonlinear terms. The addressed model contains a nonlocal nonlinear damping term which generalizes some classes of dissipations usually given in the literature, namely, the linear, the nonlinear and the nonlocal frictional ones. A first mathematical analysis of such damping term is presented and represents the main novelty in our approach.

MSC:

35Q74 PDEs in connection with mechanics of deformable solids
35B40 Asymptotic behavior of solutions to PDEs
35B41 Attractors
37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems
35L75 Higher-order nonlinear hyperbolic equations
74H40 Long-time behavior of solutions for dynamical problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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