Geodesic
Uniqueness of the Solution of the Inverse Problem for a Model of the Dynamics of an Age-Structured Population
Matematičeskie zametki, Tome 111 (2022) no. 1, pp. 125-133

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For the McKendrick model of the dynamics of an age-structured population, we consider the inverse problem of reconstructing two coefficients of the model: in the equation and in the nonlocal boundary condition of integral form. The values of the solution on a part of the boundary are used as the additional information in the inverse problem. We obtain conditions for the sought coefficients to be uniquely determined. The derived integral formulas can be used to solve the inverse problem numerically by the iteration method, taking into account the fact that the inverse problem is ill posed.
Keywords: inverse problem, population dynamics model, age-structured model. 
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     author = {A. Yu. Shcheglov},
     title = {Uniqueness of the {Solution} of the {Inverse} {Problem} for a {Model} of the {Dynamics} of an {Age-Structured} {Population}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {125--133},
     publisher = {mathdoc},
     volume = {111},
     number = {1},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2022_111_1_a11/}
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A. Yu. Shcheglov. Uniqueness of the Solution of the Inverse Problem for a Model of the Dynamics of an Age-Structured Population. Matematičeskie zametki, Tome 111 (2022) no. 1, pp. 125-133. http://geodesic.mathdoc.fr/item/MZM_2022_111_1_a11/