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We consider a thermo-elastic plate system where the elastic equation does not account for rotational forces. We select the case of hinged mechanical B.C. and Neumann thermal B.C., which are coupled on the boundary. We show that the corresponding s.c. contraction semigroup (on a natural energy space) is analytic and, hence, uniformly stable. Because of the… (More)

Part I: The need for differential geometry in the control of PDEs. Its main features . . . . . . . . . . . . . . . . . . . . . . . . 3 0 Informal overview of some control theory concepts and terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

We consider mixed problems for the Kirchhoff elastic and thermoelastic systems, subject to boundary control in the clamped boundary conditions BC (clamped control). If w denotes the elastic displacement and θ the temperature, we establish sharp regularity of {w,wt ,wtt } in the elastic case, and of {w,wt ,wtt ,θ} in the thermoelastic case. Our results… (More)

We consider a dynamic linear shallow shell model, subject to nonlinear dissipation active on a portion of its boundary in physical boundary conditions. Our main result is a uniform stabilization theorem which states a uniform decay rate of the resulting solutions. Mathematically, the motion of a shell is described by a system of two coupled partial… (More)

It is shown that on certain Banach spaces, including C[0,1] and L1[0,1], there is no strongly continuous semigroup (Tt )0<t<1 consisting of weakly compact operators such that (Tt )0<t<1 is an R-bounded family. More general results concerning approximating sequences are included and some variants of R-boundedness are also discussed. 2004 Elsevier Inc. All… (More)

- M. Eller, R. Triggiani
- 2000

Model of Non-homogeneous Problem (3.2) This is given explicitly in [E-L-T.2]. 4. CONSEQUENCE OF THE STRUCTURAL DECOMPOSITION: A STRATEGY FOR THE CONTROLLABILITY PROBLEM 4.0. Preliminaries [L-T.7 Sect. 6] presents a strategy, essentially already used in [LT.3, pp. 119–120], to obtain an exact controllability (surjectivity) result. In the present case of… (More)

- Shitao Liu, Roberto Triggiani
- SIAM J. Math. Analysis
- 2011

This work concerns with the existence of the time optimal controls for some linear evolution equations without the a priori assumption on the existence of admissible controls. Both global and local existence results are presented. Some necessary conditions, sufficient conditions, and necessary and sufficient conditions for the existence of time optimal… (More)

- F. BUCCI, R. TRIGGIANI
- 2002

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- Irena Lasiecka, Roberto Triggiani, P. Yao
- Control of Distributed Parameter and Stochastic…
- 1998