Ingham type approach for uniform observability inequality of the semi-discrete coupled wave equations
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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.
CitationJúnior, 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. Electronic Journal of Differential Equations, 2020(127), pp. 1-28.
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