Strong continuity of the solution to the Lyapunov equation \(XL-BX=C\) relative to an elliptic operator L

DOI10.3792/pjaa.65.70zbMath0702.35069OpenAlexW2076995222MaRDI QIDQ914959

Takao Nambu

Publication date: 1989

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pjaa.65.70

zbMATH Keywords

Lyapunov equationfractional powers of operatorsstrongly continuousgeneralized Neumann boundary conditionparabolic boundary control system

Mathematics Subject Classification ID

Control/observation systems governed by partial differential equations (93C20) Boundary value problems for second-order elliptic equations (35J25) Linear operators on function spaces (general) (47B38) Equations involving linear operators, with operator unknowns (47A62) Perturbations in context of PDEs (35B20)

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Cites Work

• On the operator equation \(BX - XA = Q\)
• An extension of stabilizing compensators for boundary control systems of parabolic type
• A generalization of the Heinz inequality
• The Ljapunov equation and an application to stabilisation of one-dimensional diffusion equations
• Elliptic Partial Differential Equations of Second Order
• Concrete characterization of the domains of fractional powers of some elliptic differential operators of the second order
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