Affiliation:
1. Department of Mathematics, Faculty of Sciences, Ibn Zohr University, Hay Dakhla, BP8106, 80000–Agadir, Morocco
Abstract
<p style='text-indent:20px;'>In this paper, we consider a spatially and size structured population model with unbounded birth process. Firstly, the model is transformed into a closed-loop system, and hence the well-posedness is established by using the feedback theory of regular linear systems. Moreover, the solution to the resulting closed-loop system is given by a perturbed semigroup. Secondly, we give a condition on birth and death rates in such a way that the solution decays exponentially. To do this, we show that the semigroup solution is positive and hence we derive a characterization of exponential stability due to the technique tools of positive semigroups. We mention that our results extend a previous work in [D. Yan and X. Fu, Comm. Pure Appl. Anal. 15 (2016), 637–655] to the unbounded situation.</p>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics
Reference24 articles.
1. D. M. Auslander, G. F. Oster, C. B. Huffaker.Dynamics of interacting populations, J. Franklin Inst., 297 (1974), 345-376.
2. G. D. Blasio.Nonlinear age-dependent population growth with history-dependent birth rate, Math. Biosci., 46 (1979), 279-291.
3. A. Boulouz, H. Bounit and S. Hadd, Feedback theory approach to positivity and stability of evolution equations, Syst & Control Lett., 161 (2022) 105167.
4. K. J. Engel and R. Nagel, One-Parameter Semigroups for Linear Systems, New York, Springer-Verlag, 2000.
5. J. Z. Farkas.Stability conditions for a nonlinear size-structured model, Nonlinear Anal. Real World Appl., 6 (2005), 962-969.
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