Ingham type approach for uniform observability inequality of the semi-discrete coupled wave equations
Date
2020-12-22
Authors
Junior, Dilberto da Silva Almeida
Ramos, Anderson de Jesus Araujo
Pantoja Fortes, Joao Carlos
Santos, Mauro de Lima
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
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.
Description
Keywords
Coupled wave equations, Positivity-preserving, Semi-discretization, Ingham's inequality
Citation
Júnior, D. S. A., Ramos, A. J. A., Fortes, J. C. P., & Santos, M. L. (2020). Ingham type approach for uniform observability inequality of the semi-discrete coupled wave equations. <i>Electronic Journal of Differential Equations, 2020</i>(127), pp. 1-28.
Rights
Attribution 4.0 International