Optimal decay rates of a nonlinear suspension bridge with memories. (English) Zbl 1479.35084
Summary: In this paper, we investigate the decay properties of suspension bridge with memories in one dimension. To prove our results, we use the energy method to build some very delicate Lyapunov functionals that give the desired results.
MSC:
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35L53 | Initial-boundary value problems for second-order hyperbolic systems |
| 35L71 | Second-order semilinear hyperbolic equations |
| 35L76 | Higher-order semilinear hyperbolic equations |
| 35R09 | Integro-partial differential equations |
| 74D99 | Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials) |
| 93D15 | Stabilization of systems by feedback |
| 93D20 | Asymptotic stability in control theory |
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