Existence result for inverse problems governed by generalized rayleigh-tokes equations

Abstract

In this article, we study an inverse source problem related to the generalized Rayleigh–Stokes equations on Hilbert scales, with weak-valued nonlinearities and memory effects depending on the history of the state function. We establish a representation of the mild solution and then investigate crucial properties of the associated resolvent operators. Based on these analyses, the existence result is obtained by applying Banach’s fixed-point principle. Finally, an illustrative example is provided to demonstrate the theoretical results.