Analysis of an optimal control problem for the three-dimensional coupled modified Navier-Stokes and Maxwell equations

DOI10.1016/j.jmaa.2006.10.053zbMath1158.49003OpenAlexW2145460776MaRDI QIDQ886182

Max D. Gunzburger, Cǎ tǎ lin Trenchea

Publication date: 26 June 2007

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2006.10.053

zbMATH Keywords

optimal controlMaxwell equationsmagnetohydrodynamicsGâteaux derivativesmodified Navier-Stokes equations

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Navier-Stokes equations for incompressible viscous fluids (76D05) Navier-Stokes equations (35Q30) Existence theories for optimal control problems involving partial differential equations (49J20)

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Cites Work

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• Finite element approximation of the Navier-Stokes equations
• The boundary value problems of mathematical physics. Transl. from the Russian by Jack Lohwater
• Some analytic and geometric properties of the solutions of the evolution Navier-Stokes equations
• Modelling control of crystal growth processes
• On the global unique solvability of initial-boundary value problems for the coupled modified Navier-Stokes and Maxwell equations
• Boundary optimal control of MHD flows
• Linear and quasilinear elliptic equations
• Optimal Control for a Stationary MHD System in Velocity‐Current Formulation
• Boundary optimal control for an electrically conducting fluid using boundary electrical potential controls
• Real-Time Computational Algorithm for Optimal Control of an MHD Flow System

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