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1-d Wave Equations Coupled via Viscoelastic Springs and Masses: Boundary Controllability of a Quasilinear and Exponential Stabilizability of a Linear Model

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Trends in Control Theory and Partial Differential Equations

Part of the book series: Springer INdAM Series ((SINDAMS,volume 32))

Abstract

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.

Yue Wang—Project supported by the DFG EXC315 Engineering of Adcanced Materials, National Basic Research Program of China (No 2013CB834100), and the National Natural Science Foundation of China (11121101).

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Correspondence to Günter Leugering .

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Leugering, G., Li, T., Wang, Y. (2019). 1-d Wave Equations Coupled via Viscoelastic Springs and Masses: Boundary Controllability of a Quasilinear and Exponential Stabilizability of a Linear Model. In: Alabau-Boussouira, F., Ancona, F., Porretta, A., Sinestrari, C. (eds) Trends in Control Theory and Partial Differential Equations. Springer INdAM Series, vol 32. Springer, Cham. https://doi.org/10.1007/978-3-030-17949-6_8

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