| Abstract: |
| We consider an optimal control problem for semilinear parabolic equations with infinite horizon, pointwise state contraints and two different types of control constraints (pointwise in space and time, and pointwise in time and $L^2$ in space). We present new results on first-order necessary conditions and second-order sufficient condition for local optimality. We also address the approximation of the infinite horizon control problem by finite horizon problems. We analyze the convergence of these approximations and provide error estimates. |
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