Geodesic
Identification of the local changes in age-structured population dynamics with missing initial condition
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2024), pp. 3-19 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, we study an inverse problem consisting of determining the unknown local changes of a population densities independent of the missing initial population age distribution from the knowledge of some measurement in the state. The main idea is to transform the study of the inverse problem into an optimal control problem with incomplete data. To solve this kind of problem, we use the method of no-regret control approximated by a sequence of low-regret control. We show the existence and uniqueness of the sequence of low-regret control, which converges weakly to the unique no-regret control. The local changes are characterized by a coupled optimality system.
Keywords: identification problem, age-structured population, incomplete data, no-regret control, coupled optimality system. 
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F. Achab; A. Hafdallah; I. Rezzoug. Identification of the local changes in age-structured population dynamics with missing initial condition. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2024), pp. 3-19. http://geodesic.mathdoc.fr/item/IVM_2024_8_a0/

[1] Shapiro A.P., Luppov S.P., Rekurrentnye uravneniya v teorii populyatsionnoi biologii, Nauka, M., 1983 | MR

[2] Ainseba B., Anita S., “Local exact controllability of the age-dependent population dynamics with diffusion”, Abstract and Appl. Anal., 6:6 (2001), 357–368 | DOI | MR | Zbl

[3] Kang H., Ruan S., Yu X., “Age-Structured Population Dynamics with Nonlocal Diffusion”, J. Dynamics and Diff. Equat., 34:2 (2022), 789–823 | DOI | MR | Zbl

[4] Gyllenberg M., Osipov A., Päivärinta L. “The inverse problem of linear age-structured population dynamics”, J. Evolution Equat., 2 (2002), 223–239 | DOI | MR

[5] Andrusyak R.V., “Inverse problem for a physiologically structured population model with variable-effort harvesting”, Open Math., 15:1 (2017), 433–445 | DOI | MR | Zbl

[6] Yang L., Yu J.N., Deng Z.C., “An inverse problem of identifying the coefficient of parabolic equation.”, Appl. Math. Model., 32:10 (2008), 1984–1995 | DOI | MR | Zbl

[7] Lions J.L., “Contrôle à moindres regrets des systèmes distribués”, Comptes rendus de l'Académie des sciences. Sér. 1, Math., 315:12 (1992), 1253–1257 | MR | Zbl

[8] Nakoulima O., Omrane A., Velin J., “No-regret control for nonlinear distributed systems with incomplete data”, J. Math. Pures et Appl., 81:11 (2002), 1161–1189 | DOI | MR | Zbl

[9] Nakoulima O., Omrane A., Velin J., “On the Pareto Control and No-Regret Control for Distributed Systems with Incomplete Data”, SIAM J. Control and Optimization, 42:4 (2003), 1167–1184 | DOI | MR | Zbl

[10] Baleanu D., Joseph C., Mophou G., “Low-regret control for a fractional wave equation with incomplete data”, Advances Diff. Equat., 2016, no. 1, 1–20 | MR

[11] Dinakar V., Balan N.B., Balachandran K., “Identification of Source Terms in a Coupled Age-structured Population Model with Discontinuous Diffusion Coefficients”, AIMS Math., 2:1 (2017), 81–95 | DOI | MR | Zbl

[12] Djida J., Soh P.F., Mophou G.M., Optimal control of diffusion equation with missing data governed by Dirichlet fractional Laplacian, 2018, arXiv: 1809.00917 | Zbl

[13] Hafdallah A., Ayadi A., “Optimal control of electromagnetic wave displacement with an unknown velocity of propagation”, Int. J. Control, 92:11 (2018), 2693–2700 | DOI | MR

[14] Hafdallah A., “On the optimal control of linear systems depending upon a parameter and with missing data”, Nonlinear Stud., 27:2 (2020), 457–469 | MR | Zbl

[15] Hafdallah A., Ayadi A., “Optimal control of a thermoelastic body with missing initial conditions”, Int. J. Control, 93:7 (2018), 1570–1576 | DOI | MR

[16] Achab F., Iqbal B., Rezzoug I., Oussaeif T., Adel O., “Solvability and Weak Controllability of Fractional Degenerate Singular Problem”, JRC, 5:2 (2024)

[17] Hafdallah A., “Identification of diffusion coefficient in a semi-linear parabolic equation with incomplete initial condition: a no-regret control method”, J. Control and Decision, 2023 | DOI

[18] Laouar C., Ayadi A., Hafdallah A., “Optimal Control of a Partially Known Coupled System of BOD an DO”, Int. J. Anal. and Appl., 19:6 (2021), 984–996 | DOI

[19] Touchette H., Legendre–Fenchel transforms in a nutshell, , 2005 https://appliedmaths.sun.ac.za/h̃touchette/archive/notes/lfth2.pdf