Applied Mathematics and Optimization, Vol.47, No.2, 121-142, 2003
Existence of optimal controls for semilinear parabolic equations without Cesari-type conditions
Optimal control problems governed by semilinear parabolic partial differential equations are considered. No Cesari-type conditions are assumed. By proving the existence theorem and the Pontryagin maximum principle of optimal "state-control" pairs for the corresponding relaxed problems, an existence theorem of optimal pairs for the original problem is established.