Electronic Journal of Differential Equations, Vol. 2021 (2021), No. 60, pp. 1-12.

Title: Controllability for the wave equation with moving boundary
       
Authors: Isaias  P. de Jesus (Univ. Federal do Piaui, PI, Brazil)
         Eugenio Cabanillas Lapa (Univ. Nacional Mayor de San Marcos, Lima, Peru)
         Juan Limaco (Univ. Federal Fluminense,  Niteroi, RJ, Brazil)

Abstract: 
 In this article, we study the boundary controllability for a one-dimensional string
 equation on a domain with time-dependent boundary. This equation models small vibrations
 of a string with one of its endpoint fixed and other moving with speed k(t).
 We use an inverse inequality  to obtain a controllability result.  We consider a linear
 wave equation.

Submitted November 1, 2020. Published July 5, 2021.
Math Subject Classifications: 93B05, 93C05, 93C20.
Key Words: Wave equation; Stackelberg-Nash strategies; controllability; inverse inequality.