Journal
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
Volume 74, Issue 2, Pages 585-599Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.na.2010.09.014
Keywords
Multi-phase fluids; Optimal control; Optimality system; Artificial diffusion; Renormalized solution
Categories
Funding
- SFB Mathematical Optimization and Applications in Biomedical Sciences, Fonds zur Forderung der wissenschaftlichen Forschung, Austria
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Optimal control for a system consistent of the viscosity dependent Stokes equations coupled with a transport equation for the viscosity is studied. Motivated by a lack of sufficient regularity of the adjoint equations, artificial diffusion is introduced to the transport equation. The asymptotic behavior of the regularized system is investigated. Optimality conditions for the regularized optimal control problems are obtained and again the asymptotic behavior is analyzed. The lack of uniqueness of solutions to the underlying system is another source of difficulties for the problem under investigation. Crown Copyright (C) 2010 Published by Elsevier Ltd. All rights reserved.
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