An adjoint control method for initial condition identification of the   Abstract Cauchy problem
  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. 
Cary Humber, Kazufumi Ito
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