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.

scholarly journals First Boundary Value Problem for Cordes-Type Semilinear Parabolic Equation with Discontinuous Coefficients

2020 ◽  
Vol 2020 ◽  
pp. 1-4
Author(s):  
Aziz Harman ◽  
Ezgi Harman
Keyword(s):  
Parabolic Equation ◽  
Parabolic Equations ◽  
Discontinuous Coefficients ◽  
Semilinear Parabolic Equation ◽  
Semilinear Parabolic Equations ◽  
Strong Solvability ◽  
Carathéodory Function ◽  
The Subject ◽  
Cordes Condition ◽  
Semilinear Parabolic

For a class of semilinear parabolic equations with discontinuous coefficients, the strong solvability of the Dirichlet problem is studied in this paper. The problem ∑i,j=1naijt,xuxixj−ut+gt,x,u=ft,x,uΓQT=0, in QT=Ω×0,T is the subject of our study, where Ω is bounded C2 or a convex subdomain of En+1,ΓQT=∂QT\∖t=T. The function gx,u is assumed to be a Caratheodory function satisfying the growth condition gt,x,u≤b0uq, for b0>0,q∈0,n+1/n−1,n≥2, and leading coefficients satisfy Cordes condition b0>0,q∈0,n+1/n−1,n≥2.

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