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.

Classification: 49K20, 35B27

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}, publisher = {EDP-Sciences}, volume = {17}, number = {4}, year = {2011}, pages = {975-994}, doi = {10.1051/cocv/2010034}, zbl = {1238.49033}, mrnumber = {2859861}, language = {en}, url = {http://www.numdam.org/item/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/item/COCV_2011__17_4_975_0/

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