| Abstract: |
| Inverse problems play an important role in mathematics and its applications, as they aim to determine unknown components of a system from indirect observations. Such problems become particularly challenging when the underlying dynamics involve delays and degeneracy, which frequently appear in models with memory and singular behaviour. In this talk, we consider a first-order identification problem for a class of abstract degenerate delay differential equations in a Banach space. The main objective is to determine unknown elements of the system dynamics using additional observational data. Under suitable assumptions on closed linear operators, the degenerate problem can be reduced to an equivalent nondegenerate formulation, which allows us to establish the unique solvability of the identification problem. The more general situation is then analyzed using recent results concerning convolution techniques, which enable the simultaneous treatment of delay effects and degeneracy. Finally, an example is presented to illustrate the applicability of the abstract results and to demonstrate their validity. |
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