Differential and Integral Equations

Explicit construction of a boundary feedback law to stabilize a class of parabolic equations

Abdelhadi Elharfi

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Abstract

In this paper, a problem of boundary feedback stabilization for a class of parabolic equations is considered. The problem is reformulated to convert a parabolic equation into a well known one by using an integral transformation with a kernel required to satisfy an appropriate partial differential equation (PDE). The well-posedness of the kernel PDE and the smoothness of the solution are studied. By varying a parameter ${\lambda}>0$ in the kernel PDE, the solution is exploited to explicitly construct a boundary feedback law such that the solution of the closed loop system decays exponentially at the desired rate of ${\lambda}.$ Moreover, a control which, simultaneously, stabilizes the output function and minimizes an appropriate cost functional is derived.

Article information

Source
Differential Integral Equations, Volume 21, Number 3-4 (2008), 351-362.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356038784

Mathematical Reviews number (MathSciNet)
MR2484013

Zentralblatt MATH identifier
1224.35173

Subjects
Primary: 35K20: Initial-boundary value problems for second-order parabolic equations
Secondary: 49J20: Optimal control problems involving partial differential equations 93C20: Systems governed by partial differential equations 93D15: Stabilization of systems by feedback

Citation

Elharfi, Abdelhadi. Explicit construction of a boundary feedback law to stabilize a class of parabolic equations. Differential Integral Equations 21 (2008), no. 3-4, 351--362. https://projecteuclid.org/euclid.die/1356038784


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