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2008, Volume 7, Issue 3: 491-512. Doi: 10.3934/cpaa.2008.7.491
This issue Previous Article Global existence and scattering for rough solutions to generalized nonlinear Schrödinger equations on $R$ Next Article On the decay in time of solutions of some generalized regularized long waves equations

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

  • 2.

    Faculty of Mathematics, University “Al.I. Cuza” and, Institute of Mathematics “Octav Mayer”, Iaşi 700506

Received:  January 31, 2007
Revised:  July 31, 2007
Published:  April 2008
Abstract Related Papers Cited by
    Abstract
  • 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.
    Mathematics Subject Classification: Primary: 35K05, 35P15, 93D15, 92D25; Secondary: 35B37.

    Citation:
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