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 reaction-diffusion 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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