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Two identification issues in inverse problems discussed in this monograph.One is identifying parameters for a class abstract parabolic partial differential equations on Lipschitz continuity.In variational method framework at (complex) Hilbert spaces,applying theoretic results to Hopfield neural network;Cahn-Hilliard equation;Klein-Gordon-Schrodinger equation.Another is time independent coefficient inverse,using Taylor expansion to construct approximate polynomial for convexificaiton approach in global convergent algorithm for 2D parabolic problems.In recovery,determining and reconstructing of system profile,property or characterization,this book captured general issues to identify unknown factors.Proposed abstract theory, bi-quadratic polynomial methodology can be developed to elliptic/hyperbolic issue,or extended to 3D.Rest work focus on time-spatial wise coefficients inverse.To be practical applied to a broad diverse problems in a variety disciplinary.These kinds of behaviors to do certification (e.g.DNA) just like detector to find mystery from witness or doctor to seek sick from symptoms,delighted and stimulated.A great interest would be made sure in the future inverse problems.