Positive stabilization of a parabolic equation by controls localized on a curve

We consider the stabilization of the nonnegative solutions of linear parabolic equation by controls localized on a curve. The main results of the article give a necessary and sufficient condition for positive stabilizability in terms of the principal eigenvalue of a certain elliptic operator. In case of positive stabilizability, some feedback stabilizing controls are indicated.  2003 Elsevier Inc. All rights reserved.