Abstract:
For a population dynamics model with age structuring in a quasi-stable version, the inverse problem of restoring two coefficients of the model is considered. In the framework
of the inverse problem, the intensity of cell mortality that depends only on time and is
uniform in terms of cell age, which is included in the transfer equation, and the density of
cell reproduction that depends only on their age, located in a boundary condition of the
integral form, are determined. To determine the two desired coefficients of the model, an
additional information is required in the form of solution of the direct problem for fixed
values of one of its arguments. The uniqueness theorems of solutions to inverse problems
of determining coefficients in the equation and in the integral form boundary condition
are formulated and proved. In this case, the properties of the solution of the direct problem and the conditions for its solvability are pre-established. The integral formulas obtained during the analysis of the statements of direct and inverse problems allow us to organize various types of iterative algorithms for numerical solutions of the direct problem
and the coefficient inverse problems for obtaining approximate solutions of both direct
and inverse problems. The possibilities of using such an iterative numerical solution of
coefficient inverse problems should be linked to the ill posedness of the inverse tasks.
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