Hamiltonian Pontryagin's Principles for Control Problems Governed by Semilinear Parabolic Equations

1999 ◽  
Vol 39 (2) ◽  
pp. 143-177 ◽  
Author(s):  
J. P. Raymond ◽  
H. Zidani
Keyword(s):  
Parabolic Equations ◽  
Control Problems ◽  
Semilinear Parabolic Equations ◽  
Semilinear Parabolic

scholarly journals Existence of the Optimal Control for Stochastic Boundary Control Problems Governed by Semilinear Parabolic Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Weifeng Wang ◽  
Baobin Wang
Keyword(s):  
Boundary Condition ◽  
Optimal Control ◽  
Parabolic Equations ◽  
Control Variable ◽  
Control Problems ◽  
Semilinear Parabolic Equation ◽  
Semilinear Parabolic Equations ◽  
Boundary Control Problems ◽  
Semilinear Parabolic ◽  
Stochastic Boundary

We study an optimal control problem governed by a semilinear parabolic equation, whose control variable is contained only in the boundary condition. An existence theorem for the optimal control is obtained.

scholarly journals Superconvergence for General Convex Optimal Control Problems Governed by Semilinear Parabolic Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Yongquan Dai ◽  
Yanping Chen
Keyword(s):  
Optimal Control ◽  
Parabolic Equations ◽  
Optimal Control Problems ◽  
Control Variable ◽  
The State ◽  
Control Problems ◽  
Element Approximation ◽  
Semilinear Parabolic Equations ◽  
State Variables ◽  
Semilinear Parabolic

We will investigate the superconvergence for the semidiscrete finite element approximation of distributed convex optimal control problems governed by semilinear parabolic equations. The state and costate are approximated by the piecewise linear functions and the control is approximated by piecewise constant functions. We present the superconvergence analysis for both the control variable and the state variables.

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