Identification Problem for Strongly Degenerate EvolutionEquations with the Gerasimov–Caputo Derivative
2020
For a linear differential equation in a Banach space with a degenerate operator multiplying
the fractional Gerasimov–Caputo derivative, we prove a theorem on the existence of a unique
solution of the inverse problem with an unknown time-dependent coefficient. It is assumed that
the relative boundedness condition is satisfied for the pair of operators occurring in the equation
and an overdetermation condition with an operator whose kernel contains the degeneracy
subspace of the equation under study is specified. The result obtained is illustrated with an
example of a model system of partial differential equations unsolved for the fractional time
derivative, containing an unknown coefficient, and equipped with initial and boundary conditions
and an overdetermination condition.
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