Internal observability for coupled systems of linear partial differential equations

Lissy P, Zuazua E (2019)

Publication Type: Journal article

Publication year: 2019

Journal

SIAM Journal on Control and Optimization Society for Industrial and Applied Mathematics

Book Volume: 57

Pages Range: 832-853

Journal Issue: 2

DOI: 10.1137/17M1119160

Abstract

We deal with the internal observability for some coupled systems of partial differential equations with constant or time-dependent coupling terms by means of a reduced number of observed components. We prove new general observability inequalities under some Kalman-like or Silverman-Meadows-like condition. Our proofs combine the observability properties of the underlying scalar equation with algebraic manipulations. In the more specific case of systems of heat equations with constant coefficients and nondiagonalizable diffusion matrices, we also give a new necessary and sufficient condition for observability in the natural L2-setting. The proof relies on the use of the Lebeau-Robbiano strategy together with a precise study of the cost of controllability for linear ordinary differential equations, and allows us to treat the case where each component of the system is observed in a different subdomain.

Authors with CRIS profile

Enrique Zuazua Iriondo

Involved external institutions

University of Paris 9 - Paris-Dauphine / Université Paris 9 Paris-Dauphine FR France (FR) University of Deusto / Universidad de Deusto ES Spain (ES)

How to cite

APA:

Lissy, P., & Zuazua, E. (2019). Internal observability for coupled systems of linear partial differential equations. SIAM Journal on Control and Optimization, 57(2), 832-853. https://dx.doi.org/10.1137/17M1119160

MLA:

Lissy, Pierre, and Enrique Zuazua. "Internal observability for coupled systems of linear partial differential equations." SIAM Journal on Control and Optimization 57.2 (2019): 832-853.

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