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We study the boundary controllability problem for a multilayer Rao-Nakra sandwich beam. This beam model consists of a Rayleigh beam coupled with a number of wave equations. We consider all combinations of clamped and hinged boundary conditions with the control applied to either the moment or the rotation angle at an end of the beam. We prove that exact controllability holds provided the damping parameter is sufficiently small. In the undamped case, exact controllability holds without any restriction on the parameters in the system. In each case, optimal control time is obtained in the space of optimal regularity for $L^2(0,T)$ controls. A key step in the proof of our main result is the proof of uniqueness of the zero solution of the eigensystem with the homogeneous boundary conditions together with zero boundary observation.
The exact distributed controllability of the semilinear wave equation $partial_{tt}y-Delta y + g(y)=f ,1_{omega}$ posed over multi-dimensional and bounded domains, assuming that $gin C^1(mathbb{R})$ satisfies the growth condition $limsup_{rto infty}
In this paper we are concerned with a two-penalty boundary obstacle problem of interest in thermics, fluid dynamics and electricity. Specifically, we prove existence, uniqueness and optimal regularity of the solutions, and we establish structural properties of the free boundary.
In this paper we study the internal exact controllability for a second order linear evolution equation defined in a two-component domain. On the interface we prescribe a jump of the solution proportional to the conormal derivatives, meanwhile a homog
Controlling complex networks is of paramount importance in science and engineering. Despite the recent development of structural-controllability theory, we continue to lack a framework to control undirected complex networks, especially given link wei
In this expository paper we survey some recent results on Dirichlet problems of the form $Lu=f(x,u)$ in $Omega$, $uequiv0$ in $mathbb R^nbackslashOmega$. We first discuss in detail the boundary regularity of solutions, stating the main known results