Applied Mathematics & Optimization

, Volume 75, Issue 2, pp 151–173 | Cite as

Optimal Wentzell Boundary Control of Parabolic Equations

  • Yousong LuoEmail author


This paper deals with a class of optimal control problems governed by an initial-boundary value problem of a parabolic equation. The case of semi-linear boundary control is studied where the control is applied to the system via the Wentzell boundary condition. The differentiability of the state variable with respect to the control is established and hence a necessary condition is derived for the optimal solution in the case of both unconstrained and constrained problems. The condition is also sufficient for the unconstrained convex problems. A second order condition is also derived.


Optimality condition Parabolic equation Boundary control Wentzell boundary condition 

Mathematics Subject Classification

49K20 35K20 


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.School of Mathematical and Geospatial SciencesRMIT UniversityMelbourneAustralia

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