Translator Disclaimer
2008 Explicit construction of a boundary feedback law to stabilize a class of parabolic equations
Abdelhadi Elharfi
Differential Integral Equations 21(3-4): 351-362 (2008).

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.

Citation

Download Citation

Abdelhadi Elharfi. "Explicit construction of a boundary feedback law to stabilize a class of parabolic equations." Differential Integral Equations 21 (3-4) 351 - 362, 2008.

Information

Published: 2008
First available in Project Euclid: 20 December 2012

zbMATH: 1224.35173
MathSciNet: MR2484013

Subjects:
Primary: 35K20
Secondary: 49J20, 93C20, 93D15

Rights: Copyright © 2008 Khayyam Publishing, Inc.

JOURNAL ARTICLE
12 PAGES


SHARE
Vol.21 • No. 3-4 • 2008
Back to Top