Electron. J. Differential Equations, Vol. 2021 (2021), No. 60, pp. 1-12.

Controllability for the wave equation with moving boundary

Isaias P. de Jesus, Eugenio Cabanillas Lapa, Juan Limaco

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.

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Isaías P. de Jesus
Universidade Federal do Piauí,
DM, Teresina, PI, Brazil
email: isaias@ufpi.edu.br
Eugenio Cabanillas Lapa
Universidad Nacional Mayor de San Marcos
Facultad de Ciencias Matem\áticas
Instituto de Investigación, Lima, Perú
email: cleugenio@yahoo.com
Juan Limaco
Universidade Federal Fluminense
IME, Niterói, RJ, Brazil
email: jlimaco@id.uff.br

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