Optimal control of partial differential equations

Part of the MS&A book series (MS&A, volume 2)


In this chapter we will introduce the basic concepts of optimal control for linear elliptic partial differential equations. At first we present the classical theory in functional spaces “à la J.L.Lions”, see [Lio71] and [Lio72]; then we will address the methodology based on the use of the Lagrangian functional (see, e.g., [Mau81], [BKR00] and [Jam88]). Finally, we will show two different numerical approaches for control problems, based on the Galerkin finite element method.


Control Problem Variational Inequality Optimal Control Problem Control Function Forced Convection 
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© Springer-Verlag Italia, Milan 2009

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