Skip to Main content Skip to Navigation
Journal articles

Internal observability for coupled systems of linear partial differential equations

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 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.
Document type :
Journal articles
Complete list of metadata

Cited literature [49 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01480301
Contributor : Pierre Lissy <>
Submitted on : Sunday, April 15, 2018 - 10:29:00 AM
Last modification on : Monday, December 14, 2020 - 5:26:10 PM

File

ObsCoupled.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01480301, version 2

Citation

Pierre Lissy, Enrique Zuazua. Internal observability for coupled systems of linear partial differential equations. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2019, 57 (2), pp.832-853. ⟨hal-01480301v2⟩

Share

Metrics

Record views

573

Files downloads

887