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homogenized spike variation

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Optimality conditions for semilinear parabolic equations withcontrols in leading term *
Hongwei Lou
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 17 / Issue 4 / October 2011

Published online by Cambridge University Press:

23 August 2010, pp. 975-994

Print publication:

October 2011
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An optimal control problem forsemilinear 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 themethod of homogenizing spike variation. Results for problems withstate constraints are also stated.