An adjoint control method for initial condition identification of the Abstract Cauchy problem
arXiv:1202.5263h-index: 50
Analysis pending
This paper develops and analyzes a generic method for reconstructing solutions to the abstract Cauchy problem in a general Hilbert space, from noisy measured data. The method is based on the relationship between a partial differential equation and its adjoint equation with control. We demonsrate the capability of the method through analysis and numerical experiments.