Abstract
We consider the classical Gurtin–MacCamy system describing the growth and spread of an age structured population and show that the steady states are actually stabilizable by a controller v = v(a, t) acting on an age interval [a 1, a 2].
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Barbu V., Triggiani R.: Internal stabilization of Navier-Stokes equations with finite-dimensional controllers. Indiana Univ. Math. J. 53, 1443–1494 (2004)
Barbu V., Wang G.: Internal stabilization of semi-linear parabolic systems. J. Math. Anal. Appl. 285, 387–407 (2003)
Bensoussan A., Da Prato G., : Internal stabilization of Navier-Stokes equations with finite-dimensional controllers. Indiana Univ. Math. J. 53, 1443–1494 (2004)
Iannelli M., Mathematical Theory of Age-Structured Population Dynamics, Applied Mathematics Monograph C.N.R. vol. 7, Giardini editori e stampatori, Pisa 1995 Giardini
T. Kato, Perturbation Theory for Linear Operators, Springer Verlag 1976.
Triggiani R.: Boundary feedback stabilizability of parabolic systems. Appl. Math. Optimiz. 6, 201–220 (1980)
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was performed when visiting the University of Trento within the “Ateneo Visiting Program 2008” and partially supported by Grant 2EEx-06-D11-97/2006 of Romanian Ministery of Research
Rights and permissions
About this article
Cite this article
Iannelli, M., Barbu, V. Stabilization of the Gurtin–MacCamy population system. J. Evol. Equ. 9, 727 (2009). https://doi.org/10.1007/s00028-009-0031-9
Published:
DOI: https://doi.org/10.1007/s00028-009-0031-9