Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-25T17:37:34.684Z Has data issue: false hasContentIssue false
  • English
  • Français

APPROXIMATE CONTROLLABILITY OF POPULATION DYNAMICS WITH SIZE DEPENDENCE AND SPATIAL DISTRIBUTION

Part of: Hyperbolic equations and systems Controllability, observability, and system structure

Published online by Cambridge University Press:  16 May 2017

S. P. WANG Open the ORCID record for S. P. WANG [Opens in a new window]  and
Z. R. HE Open the ORCID record for Z. R. HE [Opens in a new window]
S. P. WANG
Affiliation:
Institute of Operational Research and Cybernetics, Hangzhou Dianzi University, Zhejiang, PR China email [email protected] email [email protected]
Z. R. HE*
Affiliation:
Institute of Operational Research and Cybernetics, Hangzhou Dianzi University, Zhejiang, PR China email [email protected] email [email protected]
*
✉[email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We investigate the approximate controllability of a size- and space-structured population model, for which the control function acts on a subdomain and corresponds to the migration of individuals. We establish the main result via the unique continuation property of the adjoint system. The desired controller is the minimizer of an infinite-dimensional optimization problem.

Keywords

size and space structurepopulation modelapproximate controllabilityfixed point theoremHilbert uniqueness method

MSC classification

Primary: 35L60: Nonlinear first-order hyperbolic equations
Secondary: 92D25: Population dynamics (general) 93B05: Controllability
Type
Research Article
Information
The ANZIAM Journal , Volume 58 , Issue 3-4 , April 2017 , pp. 474 - 481
Copyright
© 2017 Australian Mathematical Society 

References

Ainseba, B. and Langlais, M., “Sur le problème de contrôle d’une population structurée en âge et en espace”, C. R. Acad. Sci. Paris Sér. 1 323 (1996) 269–274; http://cat.inist.fr/?aModele=afficheN&cpsidt=3183008.Google Scholar
Ainseba, B. and Langlais, M., “On a population dynamics control problem with age dependence and spatial structure”, J. Math. Anal. Appl. 248 (2000) 455–474; doi:10.1006/jmaa.2000.6921.Google Scholar
Aniţa, S., Analysis and control of age-dependent population dynamics (Kluwer Academic, Dordrecht, 2000).Google Scholar
Barbu, V., Iannelli, M. and Martcheva, M., “On the controllability of the Lotka–McKendrick model of population dynamics”, J. Math. Anal. Appl. 253 (2001) 142–165; doi:10.1006/jmaa.2000.7075.Google Scholar
Boulite, S., Idrissi, A. and Maniar, L., “Controllability of semi-linear boundary problems with nonlocal initial conditions”, J. Math. Anal. Appl. 316 (2006) 566–578; doi:10.1016/j.jmaa.2005.05.006.Google Scholar
Ebenman, B. and Persson, L., Size-structured populations: ecology and evolution (Springer, Berlin–Heidelberg–New York–London, 1988).Google Scholar
Fursikov, A. V. and Imanuvilov, O. Y., Controllability of evolution equations, Volume 34 of Lecture Notes Series (Seoul National University, Seoul, Korea, 1996).Google Scholar
He, Y. and Ainseba, B., “Exact null controllability of the Lobesia botrana model with diffusion”, J. Math. Anal. Appl. 409 (2014) 530–543; doi:10.1016/j.jmaa.2013.07.020.Google Scholar
Kavian, O. and Traoré, O., “Approximate controllability by birth control for a nonlinear population dynamics model”, ESAIM Control Optim. Calc. Var. 17 (2011) 1189–1213; doi:10.1051/cocv/2010043.Google Scholar
Li, T., Exact controllability perturbation and stabilization of distributed parameter systems (Higher Education Press, Beijing, 2012).Google Scholar
Lions, J. L., Contrôlabilité exacte, perturbations et stabilisation de systèms distributés, Tome 1, Contrôlabilité exacte (Dunod, Paris, 1988).Google Scholar
Sinko, J. W. and Streifer, W., “A new model for age-size structure of a population”, Ecology 48 (1967) 910–918; http://www.jstor.org/stable/1934533.Google Scholar
Traore, O., “Approximate controllability and application to data assimilation problem for a linear population dynamics model”, IAENG Int. J. Appl. Math. 37 (2007) 1–12; http://www.iaeng.org/IJAM/issues_v37/issue_1/IJAM_37_1_01.pdf.Google Scholar
Yamamoto, M., “Carleman estimates for parabolic equations and applications”, Inverse Problems 25 (2009) 1–75; doi:10.1088/0266-5611/25/12/123013.Google Scholar