1-d wave equations coupled via viscoelastic springs and masses: boundary controllability of a quasilinear and exponential stabilizability of a linear model. (English) Zbl 1428.35235
Alabau-Boussouira, Fatiha (ed.) et al., Trends in control theory and partial differential equations. Cham: Springer. Springer INdAM Ser. 32, 139-156 (2019).
Summary: We consider the out-of-the-plane displacements of nonlinear elastic strings which are coupled through point masses attached to the ends and viscoelastic springs. We provide the modeling, the well-posedness in the sense of classical semi-global \(C^2\)-solutions together with some extra regularity at the masses and then prove exact boundary controllability and velocity-feedback stabilizability, where controls act on both sides of the mass-spring-coupling.
For the entire collection see [Zbl 1417.35002].
For the entire collection see [Zbl 1417.35002].
MSC:
| 35L72 | Second-order quasilinear hyperbolic equations |
| 93B05 | Controllability |
| 35L53 | Initial-boundary value problems for second-order hyperbolic systems |
| 74K05 | Strings |
