Geodesic
Optimal Control of Nonlinear Evolution Systems in the Case where the Solution is not Differentiable with Respect to the Control
Matematičeskie zametki, Tome 93 (2013) no. 4, pp. 586-603

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For the simplest heat equation with power nonlinearity, the dependence of the solution of the corresponding boundary-value problem on the constant term of the equation turns out to be, in general, not differentiable in the sense of Gâteaux.
Keywords: optimal control, nonlinear evolution system, heat equation with power nonlinearity, Gâteaux differentiability, Lagrange optimality principle. 
@article{MZM_2013_93_4_a9,
     author = {S. Ya. Serovaǐskiǐ},
     title = {Optimal {Control} of {Nonlinear} {Evolution} {Systems} in the {Case} where the {Solution} is not {Differentiable} with {Respect} to the {Control}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {586--603},
     publisher = {mathdoc},
     volume = {93},
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     year = {2013},
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     url = {http://geodesic.mathdoc.fr/item/MZM_2013_93_4_a9/}
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S. Ya. Serovaǐskiǐ. Optimal Control of Nonlinear Evolution Systems in the Case where the Solution is not Differentiable with Respect to the Control. Matematičeskie zametki, Tome 93 (2013) no. 4, pp. 586-603. http://geodesic.mathdoc.fr/item/MZM_2013_93_4_a9/