Abstract:
The issues of unique solvability of linear inverse coefficient problems for evolution integro-differential equations of Gerasimov type with a singular integral kernel in Banach spaces are investigated. The cases of bounded and sectorial operators at the unknown function in the equation are considered. In each case, correctness criteria were obtained for the linear inverse problem with a time-independent unknown coefficient, and sufficient conditions for solvability and correctness estimates were found for the linear identification problem with a time-dependent unknown coefficient. The abstract results obtained are illustrated by an example of a class of inverse problems for partial differential equations.
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