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Nonlinear Partial Differential Equations and Their Applications
- Publisher
- Springer Journals
- Copyright
- Copyright © 2010 by Springer Science+Business Media, LLC
- Subject
- Mathematics; Numerical and Computational Physics; Mathematical Methods in Physics; Theoretical, Mathematical and Computational Physics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization
- ISSN
- 0095-4616
- eISSN
- 1432-0606
- DOI
- 10.1007/s00245-009-9087-8
- Publisher site
- See Article on Publisher Site
Abstract
In this paper we derive a necessary optimality condition for a local optimal solution of some control problems. These optimal control problems are governed by a semi-linear Vettsel boundary value problem of a linear elliptic equation. The control is applied to the state equation via the boundary and a functional of the control together with the solution of the state equation under such a control will be minimized. A constraint on the solution of the state equation is also considered.
Journal
Applied Mathematics and Optimization – Springer Journals
Published: Jun 1, 2010