Differential and Integral Equations

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

Abdelhadi Elharfi

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

First available in Project Euclid: 20 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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

Export citation