Optimal Control of Systems Governed by Partial Differential Equations |
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Optimal Control of Systems Governed by Partial Differential Equations Jacques Louis Lions No preview available - 1971 |
Optimal Control of Systems Governed by Partial Differential Equations Jacques Louis Lions No preview available - 1971 |
Optimal Control of Systems Governed by Partial Differential Equations Jacques Louis Lions No preview available - 2011 |
Common terms and phrases
adjoint state p(u admits a unique analogous apply Theorem boundary conditions bounded set Chapter constraints continuous linear form control problems convex set convex subset cost function decoupling deduce defined denoted dt² dxdt dy(v elliptic elliptic operator equivalent example exists a unique extract a subsequence function is given Green's formula H¹(Q hence Hilbert space hypotheses identity inequalities Inf J(v introduce the adjoint L²(E L²(Q Lemma Let us assume linear Lions-Magenes non-linear notation observation obtain optimal control p(u)+Nu partial differential equations Proof of Theorem prove regular Remark resp Riccati satisfies scalar product second order system of equations systems governed Theorem 1.1 unilateral problem unique solution vead velad verify VvE Uad weak topology weakly in L²(0 whence y(to y₁ ym(t yo(x ΧΕΩ Ω Ω ди др ду ду дхо