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.

Keywords: optimal control, necessary conditions, parabolic equation, homogenized spike variation

@article{COCV_2011__17_4_975_0, author = {Lou, Hongwei}, title = {Optimality conditions for semilinear parabolic equations with controls in leading term}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {975--994}, publisher = {EDP-Sciences}, volume = {17}, number = {4}, year = {2011}, doi = {10.1051/cocv/2010034}, zbl = {1238.49033}, mrnumber = {2859861}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv/2010034/} }

TY - JOUR AU - Lou, Hongwei TI - Optimality conditions for semilinear parabolic equations with controls in leading term JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2011 SP - 975 EP - 994 VL - 17 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2010034/ DO - 10.1051/cocv/2010034 LA - en ID - COCV_2011__17_4_975_0 ER -

%0 Journal Article %A Lou, Hongwei %T Optimality conditions for semilinear parabolic equations with controls in leading term %J ESAIM: Control, Optimisation and Calculus of Variations %D 2011 %P 975-994 %V 17 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2010034/ %R 10.1051/cocv/2010034 %G en %F COCV_2011__17_4_975_0

Lou, Hongwei. Optimality conditions for semilinear parabolic equations with controls in leading term. ESAIM: Control, Optimisation and Calculus of Variations, Volume 17 (2011) no. 4, pp. 975-994. doi : 10.1051/cocv/2010034. http://www.numdam.org/articles/10.1051/cocv/2010034/

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