Optimal L1-Control in Coefficients for Dirichlet Elliptic Problems: W-Optimal Solutions
Kogut PI, Leugering G (2011)
Publication Type: Journal article
Publication year: 2011
Journal
Publisher: Springer Verlag (Germany)
Book Volume: 150
Pages Range: 205--232
Volume: 150
Issue: 2
Journal Issue: 2
DOI: 10.1007/s10957-011-9840-4
Abstract
In this paper, we study a Dirichlet optimal control problem associated with a linear elliptic equation the coefficients of which we take as controls in the class of integrable functions. The coefficients may degenerate and, therefore, the problems may exhibit the so-called Lavrentieff phenomenon and non-uniqueness of weak solutions. We consider the solvability of this problem in the class of W-variational solutions. Using a concept of variational convergence of constrained minimization problems in variable spaces, we prove the existence of W-solutions to the optimal control problem and provide the way for their approximation. We emphasize that control problems of this type are important in material and topology optimization as well as in damage or life-cycle optimization.
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APA:
Kogut, P.I., & Leugering, G. (2011). Optimal L1-Control in Coefficients for Dirichlet Elliptic Problems: W-Optimal Solutions. Journal of Optimization Theory and Applications, 150(2), 205--232. https://doi.org/10.1007/s10957-011-9840-4
MLA:
Kogut, Peter I., and Günter Leugering. "Optimal L1-Control in Coefficients for Dirichlet Elliptic Problems: W-Optimal Solutions." Journal of Optimization Theory and Applications 150.2 (2011): 205--232.
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