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Optimization problems for structural acoustic models with thermoelasticity and smart materials

Irena Lasiecka — 2000

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Optimization problem for a structural acoustic model with controls governed by unbounded operators on the state space is considered. This type of controls arises naturally in the context of "smart material technology". The main result of the paper provides an optimal synthesis and solvability of associated nonstandard Riccati equations. It is shown that in spite of the unboundedness of control operators, the resulting gain operators (feedbacks) are bounded on the state space. This allows to provide...

Sharp regularity of the second time derivative w_tt of solutions to Kirchhoff equations with clamped Boundary Conditions

Irena LasieckaRoberto Triggiani — 2001

International Journal of Applied Mathematics and Computer Science

We consider mixed problems for Kirchhoff elastic and thermoelastic systems, subject to boundary control in the clamped Boundary Conditions B.C. (“clamped control”). If w denotes elastic displacement and θ temperature, we establish optimal regularity of {w, w_t, w_tt} in the elastic case, and of {w, w_t, w_tt, θ} in the thermoelastic case. Our results complement those presented in (Lagnese and Lions, 1988), where sharp (optimal) trace regularity results are obtained for the corresponding boundary...

Blow-up of weak solutions for the semilinear wave equations with nonlinear boundary and interior sources and damping

Lorena BociuIrena Lasiecka — 2008

Applicationes Mathematicae

We focus on the blow-up in finite time of weak solutions to the wave equation with interior and boundary nonlinear sources and dissipations. Our central interest is the relationship of the sources and damping terms to the behavior of solutions. We prove that under specific conditions relating the sources and the dissipations (namely p > m and k > m), weak solutions blow up in finite time.

Optimal blowup rates for the minimal energy null control of the strongly damped abstract wave equation

George AvalosIrena Lasiecka — 2003

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

The null controllability problem for a structurally damped abstract wave equation –often referred to in the literature as a structurally damped equation– is considered with a view towards obtaining optimal rates of blowup for the associated minimal energy function min ( T ) , as terminal time T 0 . Key use is made of the underlying analyticity of the semigroup generated by the elastic operator 𝒜 , as well as of the explicit characterization of its domain of definition. We ultimately find that the blowup rate...

Exact null controllability of structurally damped and thermo-elastic parabolic models

Irena LasieckaRoberto Triggiani — 1998

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We show exact null-controllability for two models of non-classical, parabolic partial differential equations with distributed control: (i) second-order structurally damped equations, except for a limit case, where exact null controllability fails; and (ii) thermo-elastic equations with hinged boundary conditions. In both cases, the problem is solved by duality.

Uniform exponential energy decay of Euler-Bernoulli equations by suitable boundary feedback operators

Jerry BartolomeoIrena LasieckaRoberto Triggiani — 1989

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We study the uniform stabilization problem for the Euler-Bernoulli equation defined on a smooth bounded domain of any dimension with feedback dissipative operators in various boundary conditions.

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