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Optimal control problems for Kirchhoff type equation with a damping term. (English) Zbl 1190.49018
Summary: Optimal control problems are studied for the equation of Kirchhoff type with a damping term. The Gâteaux differentiability of solution mapping on control variables is proved and the various types of necessary optimality conditions corresponding to the distributive and terminal value observations are established.

49J50Fréchet and Gateaux differentiability
35L20Second order hyperbolic equations, boundary value problems
49K20Optimal control problems with PDE (optimality conditions)
35Q93PDEs in connection with control and optimization
70Q05Control of mechanical systems (general mechanics)
Full Text: DOI
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