ESAIM: Control, Optimisation and Calculus of Variations

Table of Contents - October 2011 - Volume 17, Issue 04  

Research Article

Optimality conditions for semilinear parabolic equations with controls in leading term*

Lou, Hongwei

School of Mathematical Sciences, and LMNS, Fudan University, Shanghai 200433, P.R. China. hwlou@fudan.edu.cn

Abstract

An optimal control problem for semilinear parabolic partial differential equations is considered. The control variable appears in the leading term of the equation. Necessary conditions for optimal controls are established by the method of homogenizing spike variation. Results for problems with state constraints are also stated.

(Received August 7 2009)

(Revised February 18 2010)

(Online publication August 23 2010)

Key Words:

  • Optimal control;
  • necessary conditions;
  • parabolic equation;
  • homogenized spike variation

Mathematics Subject Classification:

  • 49K20;
  • 35B27

Footnotes

*  The author was supported in part by NSFC (No. 10671040 and 10831007), and FANEDD (No. 200522).