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In this work, we have studied the quadratic cost optimal control problems and their numerical analysis of nonlinear parabolic distributed parameter systems. After established the fundamental existence and uniqueness results, we have developed the nonlinear optimal control theory for the equations having uniform Lipschitz continuous nonlinearity. Then we have applied the theoretical results to practical nonlinear parabolic partial differential equations including reactiondiffusion equations, diffusion Hopfield neural network equations. Furthermore, numerical evidences for these issues have also been solved by using variational method and finite element approach.
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