Rapid exponential stabilization of a 1-D transmission wave equation with in-domain anti-damping

Abstract

We consider the problem of pointwise stabilization of a one-dimensional wave equation with an internal spatially varying anti-damping term. We design a feedback law based on the backstepping method and prove exponential stability of the closed-loop system with a desired decay rate.

15 pages

References in corpus (1)

• Remark on the pointwise stabilization of an elastic string equation

Cited by in corpus (2)

• Stabilization for Euler-Bernoulli beam equation with a local degenerated Kelvin-Voigt damping
• Stabilization of an unstable wave equation using an infinite dimensional dynamic controller