Control of the wave equation by time-dependent coefficient

Antonin Chambolle, Fadil Santosa

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

We study an initial boundary-value problem for a wave equation with time-dependent sound speed. In the control problem, we wish to determine a sound-speed function which damps the vibration of the system. We consider the case where the sound speed can take on only two values, and propose a simple control law. We show that if the number of modes in the vibration is finite, and none of the eigenfrequencies are repeated, the proposed control law does lead to energy decay. We illustrate the rich behavior of this problem in numerical examples.

Original languageEnglish (US)
Pages (from-to)375-392
Number of pages18
JournalESAIM - Control, Optimisation and Calculus of Variations
Volume8
DOIs
StatePublished - Jun 2002

Keywords

  • Control problem
  • Damping
  • Time dependent wave equation

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