Identification of a Source Term in a Semilinear Evolution Delay Equation

Abstract

Abstract An existence, uniqueness and continuous dependence on the data result for a source term identification problem in a semilinear functional delay differential equation in a general Banach space is established. As additional condition, it is assumed that the mean of the solution, with respect to a non-atomic Borel measure, is a preassigned element in the domain of the linear part of the right-hand side of the equation. Two applications to source identification, one in a parabolic functional delay equation and another one in a hyperbolic delay equation, are also discussed.