Internal Stabilization of a Class of Parabolic Integro-Differential Equations: Application to Viscoelastic Fluids

Sheetal Dharmatti; Utpal Manna; Debopriya Mukherjee

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arXiv · 1706.05041

Internal Stabilization of a Class of Parabolic Integro-Differential Equations: Application to Viscoelastic Fluids

Sheetal Dharmatti·Utpal Manna·Debopriya Mukherjee

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Abstract

In this paper, we prove the stabilizability of abstract Parabolic Integro-Differential Equations (PIDE) in a Hilbert space with decay rate $e^{-\gamma t} $ for certain $\gamma > 0,$ by means of a finite dimensional controller in the feedback form. We determine a linear feedback law which is obtained by solving an algebraic Riccati equation. To prove the existence of the Riccati operator, we consider a linear quadratic optimal control problem with unbounded observation operator. The abstract theory of stabilization developed here is applied to specific problems related to viscoelastic fluids, e.g. Oldroyd B model and Jeffreys model.

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BibTeX RIS

Sheetal Dharmatti, Utpal Manna, Debopriya Mukherjee. 2017-06-15. Internal Stabilization of a Class of Parabolic Integro-Differential Equations: Application to Viscoelastic Fluids. https://arxiv.org/abs/1706.05041

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