An 𝐿²(Ω)-based algebraic approach to boundary stabilization for linear parabolic systems

Nambu, Takao

doi:10.1090/qam/2104271

An $L^2(\Omega )$-based algebraic approach to boundary stabilization for linear parabolic systems

Author: Takao Nambu
Journal: Quart. Appl. Math. 62 (2004), 711-748
MSC: Primary 93D15; Secondary 35K50, 47N70, 93C20
DOI: https://doi.org/10.1090/qam/2104271
MathSciNet review: MR2104271
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Abstract: We study the stabilization problem of linear parabolic boundary control systems. While the control system is described by a pair of standard linear differential operators $\left ( {L, \tau } \right )$, the corresponding semigroup generator generally admits no Riesz basis of eigenvectors. Very little information on the fractional powers of this generator is needed. In this sense our approach has enough generality as a prototype to be used for other types of parabolic systems. We propose in this paper a unified algebraic approach to the stabilization of a variety of parabolic boundary control systems.

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