By Triggiani R., Imanuvilov O., Leugering G.
In those fabrics from the convention of May-June 2003, members of those 23 papers describe their paintings on the theoretical and alertness degrees during this self-discipline that has lately elevated significantly by means of extra practical versions. basic subject matters comprise elasticity, thermo-elasticity, aero-elasticity, interactions among fluids and elastic constructions, and fluid dynamics, parabolic platforms, dynamical Lame platforms, linear and non-linear hyperbolic equations, and pseudo-differential operators on a manifold
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Additional info for Control Theory of Partial Differential Equations
It is independent of the Carleman inequality for the Stokes equation, which is necessary for the proof of local controllability. There is a large body of literature on the stabilization problem of steady-state solutions to NavierStokes equations. Here we confine ourselves to mention only a few of the papers (References 2 and 7), which are more related to this present work. We also refer to the recent paper of Fursikov  for a study of a boundary—rather than interior—problem for the Navier-Stokes equations, which, however, does not pertain to the topic of feedback stabilization in the established sense, as in the present paper.
G. Naso, Null controllability of a thermoelastic plate, Abstr. Appl. , in press.  A. Bensoussan, G. Da Prato, M. Delfour, and S. Mitter, Representation and Control of Infinte Dimensional Systems, Vol. II, Birkh¨auser, Boston, (1993).  J. Cea, Lectures on Optimization—Theory and Algorithms Published for the Tata Institute of Fundamental Research, Springer-Verlag, New York, (1978).  G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, Cambridge University Press, New York, New York, (1992).
43) a. By the regularity posted in Eq. 1, T 0 h [(G 1 − λG 2 )γ0 ϑ, φ] L 2 ( ) |h | T dt ≤ C t 0 1 4 ϑ 1− 1 2k L2( ) eA 2 x 0 t 1+ 1k 2 H dt. k Applying H¨older’s inequality to the right-hand side, with H¨older conjugates (2 2k2−1 , 1 ) now yields 1 +2−k−1 2 T 0 T h [(G 1 − λG 2 )γ0 ϑ, φ] L 2 ( ) dt ≤ C × ϑ 1− 1 2k L2( ) e A 2t 1+ 1k x0 H 2 dt ≤ C T 0 |h | h(t) 1 t 4 h(t) T k−1 −4 3 5×2k 2 −1 0 ϑ 1 −k−1 2 +2 2 L2( ) T + h(t)E 0 t dt. 1(1) 19 Because for any δ > 0, we can choose integer k large enough so that 3 5×22k −1−4 ≥ we then get k−1 T 0 h [(G 1 − λG 2 )γ0 ϑ, φ] L 2 ( ) dt ≤ C T T 15 2 − ϑ 2 L2( ) 0 T + h(t)E 0 15 2 − δ, t dt.
Control Theory of Partial Differential Equations by Triggiani R., Imanuvilov O., Leugering G.