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.


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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