Internal observability for coupled systems of linear partial differential equations - Archive ouverte HAL
Journal Articles SIAM Journal on Control and Optimization Year : 2019

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.
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Dates and versions

hal-01480301 , version 1 (01-03-2017)
hal-01480301 , version 2 (15-04-2018)

Identifiers

  • HAL Id : hal-01480301 , version 2

Cite

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