A unified and systematic optimal control theory for nonlinear Cahn-Hilliard equation is perfectly established by the means of distributed control, boundary control and initial control for abstract integral cost function and quadratic cost function in the framework of variational method in Hilbert space under weaker assumptions on exponent of nonlinearity. Computational approach is configured for semi-discrete algorithm (time-continuous, spatial discrete), and is performed using finite element method and updated conjugate gradient method to one-dimensional distributed control case. Parameter...

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...