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Keywords
(8)
Asymptotic Behavior
Optimal Control
Optimal Control Problem
Optimality Condition
Stokes Equation
Stokes Problem
Transport Equation
Uniqueness of Solution
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Optimal control for multiphase fluid Stokes problems
Optimal control for multiphase fluid Stokes problems,10.1016/j.na.2010.09.014,Nonlinear Analysistheory Methods & Applications,Karl Kunisch,Xiliang L
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Optimal control for multiphase fluid Stokes problems
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Karl Kunisch
,
Xiliang Lu
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.
Journal:
Nonlinear Analysistheory Methods & Applications  NONLINEAR ANALTHEOR METH APP
, vol. 74, no. 2, pp. 585599, 2011
DOI:
10.1016/j.na.2010.09.014
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References
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An Existence Theorem for the Multifluid NavierStokes Problem
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Journal:
Journal of Differential Equations  J DIFFERENTIAL EQUATIONS
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