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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

  • Günter LeugeringEmail author
  • Tatsien Li
  • Yue Wang
Chapter
Part of the Springer INdAM Series book 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.

Keywords

Coupled system of quasilinear wave equations Dynamical boundary condition Visoelastic springs Exact boundary controllability 

AMS subject classifications

93B05 35L05 35L72 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsFriedrich-Alexander University, Erlangen-NurembergErlangenGermany
  2. 2.School of Mathematical SciencesFudan UniversityShanghaiPeople’s Republic of China
  3. 3.Shanghai Key Laboratory for Contemporary Applied MathematicsFudan UniversityShanghaiPeople’s Republic of China
  4. 4.Nonlinear Mathematical Modeling and Methods LaboratoryFudan UniversityShanghaiPeople’s Republic of China

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