Internal observability for coupled systems of linear partial differential equations
Lissy, Pierre; Zuazua, Enrique (2019), Internal observability for coupled systems of linear partial differential equations, SIAM Journal on Control and Optimization, 57, 2, p. 832-853. https://doi.org/10.1137/17M1119160
TypeArticle accepté pour publication ou publié
External document linkhttps://hal.archives-ouvertes.fr/hal-01480301
Journal nameSIAM Journal on Control and Optimization
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Abstract (EN)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 non-diagonalizable diffusion matrices, we also give a new necessary and sufficient condition for ob-servability in the natural L 2-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 to treat the case where each component of the system is observed in a different subdomain.
Subjects / Keywordspartial differential equations; systems; observability inequalities; rank conditions
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