School of Mathematical Sciences, and LMNS, Fudan University, Shanghai 200433, P.R. China. firstname.lastname@example.org
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)
Mathematics Subject Classification:
* The author was supported in part by NSFC (No. 10671040 and 10831007), and FANEDD (No. 200522).