# American Institute of Mathematical Sciences

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May  2008, 7(3): 491-512. doi: 10.3934/cpaa.2008.7.491

## Internal nonnegative stabilization for some parabolic equations

 1 Mathématiques Appliquées de Bordeaux, UMR CNRS 5466, case 26, U.F.R. Sciences et Modélisation, Université Victor Segalen Bordeaux 2,33076 Bordeaux Cedex, France 2 Faculty of Mathematics, University “Al.I. Cuza” and, Institute of Mathematics “Octav Mayer”, Iaşi 700506

Received  February 2007 Revised  August 2007 Published  February 2008

The internal zero-stabilization of the nonnegative solutions to some parabolic equations is investigated. We provide a necessary and a sufficient condition for nonnegative stabilizability in terms of the sign of the principal eigenvalue of a certain elliptic operator. This principal eigenvalue is related to the rate of the convergence of the solution. We give some evaluations of this principal eigenvalue with respect to the geometry of the domain and of the support of the control. A stabilization result for an age-dependent population dynamics with diffusion is also established.
Citation: B. E. Ainseba, Sebastian Aniţa. Internal nonnegative stabilization for some parabolic equations. Communications on Pure and Applied Analysis, 2008, 7 (3) : 491-512. doi: 10.3934/cpaa.2008.7.491
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