Electronic Journal of Differential Equations, 
Vol. 2020 (2020), No. 127, pp. 1-28.

Title: Ingham type approach for uniform observability inequality of the semi-discrete
       coupled wave equations
       
Authors: Dilberto da Silva Almeida Junior (Federal Univ. of Para, Brazil)
         Anderson de Jesus Araujo Ramos   (Federal Univ. of Para, Brazil)
         Joao Carlos Pantoja Fortes       (Federal Univ. of Para, Brazil)
         Mauro de Lima Santos             (Federal Univ. of Para, Brazil)

Abstract:
 This article concerns an observability inequality for a system of coupled wave equations
 for the continuous models as well as for the space  semi-discrete finite difference
 approximations. For finite difference and standard finite elements methods on uniform
 numerical meshes it is known that a numerical pathology produces a blow-up of the constant
 on the observability inequality as the mesh-size tends to zero.
 We identify this numerical anomaly for coupled wave equations and we prove that there
 exists a uniform observability inequality in a subspace of solutions generated by low
 frequencies. We use the Ingham type approach for getting a uniform boundary observability.

Submitted November 14, 2019. Published December 22, 2020.
Math Subject Classifications: 35B35, 35B40, 35K57, 35Q92, 92C17.
Key Words: Coupled wave equations; positivity-preserving; semi-discretization;
           Ingham's inequality.