The aim of this paper is to prove the averaged null controllability property for a wave equation with an unknown velocity of propagation parameter and for parameter-dependent vibrating plate equation under the effect of a boundary control. The choice of the Hilbert uniqueness method seems to be the best-adapted method to our theory, where the key point to prove the desired result is an averaged inverse inequality (averaged observability inequality). Consequently, we'll prove the desired property for a large time enough and we'll design a single control chosen independently of the parameter value transferring the average of the state to the origin.
Publication Date
10/16/2020
Volume No
Issue No
DOI
10.1016/j.jmaa.2020.124697
Keywords
Averaged controllability HUM PDE depending on a parameter Averaged inverse inequality
عبدالحق حفظ الله | Abdelhak Hafdallah | 5258