# Differential Equations & Control Theory by Derek Bolton, Jonathan Hill

By Derek Bolton, Jonathan Hill

In keeping with papers on the Intl Workshop on Differential Equations and optimum regulate held lately at Ohio collage, Athens.

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Friedman, Nonlinear parabolic equations involving measures as initial conditions, J. Math. Pures Appl, 62 (1983), 73-97. [ 7 ] E. , Gale. , 2 (1997), 87-107. [ 8 ] G. Lebeau and L. Robbiano, Controle exact de 1'equation de la chaleur, Comm. Partial Diff. , 30 (1995), 335-357. L. Lions, Controlabilite exacte, stabilisation et perturbation de systemes distribues, RMA 8, Masson, Paris (1988). [10 ] J. Zabczyk, Mathematical Control Theory: An Introsuction, Birkhauser, Boston (1992). Copyright 2002 by Marcel Dekker, Inc.

E. 2) x 6 fi. e.. On the other hand, using the Fourier development for z(t) in L 2 (fi \ w ) we may infer that >Mie-A', Vi>0, where M\ > 0 is a constant. The conclusion is now obvious. e. e. x E u. Indeed, if y0(x) = 0 on a subset of cu of positive measure, then we consider the following system: yt - Ay + a(x)y = -m(x)p • x € fi, t > 0 y(x,t) =0, xQ y(x,Q) =y0(x), xeQ Copyright 2002 by Marcel Dekker, Inc. All Rights Reserved. 3) where p > 0 will be precised later and sgnLi(ul}y = \\y\\ll(a}y, if \\y\\mv) = 0.

Shubov, Well-posedness for a one dimensional nonlinear beam, in Computation and Control, IV (Bozeman, MT, 1994), Progr. Systems Control Theory, vol. 20, (Birkhauser, 1995), pp. 1-21. [3] H. T. Banks, D. S. Gilliam, and V. I. Shubov, Global solvability for damped abstract nonlinear hyperbolic systems, Differential and Integral Equations, 10 (1997), 309-332. [4] H. T. Banks, K. Ito, and Y. Wang, Well-posedness for damped second order systems with unbounded input operators, Differential and Integral Equations, 8 (1995), 587-606.