Abstract. This talk is devoted to show the different control conditions and
their implications in the Riemannian wave equations with respect to the study
of the exact control in finite time, as in the asymptotic dynamics.

References

[1] R. Triggiani and P. F. Yao, Carleman estimates with no lower-order terms for general Rie-
mann wave equations. Global uniqueness and observability in one shot, Special issue dedi-
cated to the memory of Jacques-Louis Lions. Appl. Math. Optim. 46 (2002), no. 2-3, 331375.

[2] C. Bardos, G. Lebeau and J. Rauch, Sharp sufficient conditions for the observation, control,
and stabilization of waves from the boundary, SIAM J. Control Optim., 30 (1992), 1024–1065.
[3] M. M. Cavalcanti, V. N. Domingos Cavalcanti, R. Fukuoka and J. A. Soriano, Asymptotic
stability of the wave equation on compact manifolds and locally distributed damping: a sharp
result, Arch. Ration. Mech. Anal. 197 (2010), 925–964.
[4] P. N. Seminario–Huertas, Asymptotic dynamics of wave equations on compact Riemannian
manifolds: sharp localized damping and supercritical forcing, Doctoral Dissertation, ICMC
University of S ̃ao Paulo, 2019.
[5] L. Miller, Escape function conditions for the observation, control, and stabilization of the
wave equation. SIAM J. Control Optim., 41 (2003), 1554–1566.
(P. N. Seminario–Huertas) Universidad de Chile–Facultad de Ciencias
E-mail address: Este endereço de email está sendo protegido de spambots. Você precisa do JavaScript ativado para vê-lo.