This paper is divided into two parts and focuses on the linear independence of boundary traces of eigenfunctions of boundary value problems. Part I deals with second-order elliptic operators, and Part II with Stokes (and Oseen) operators.
Part I: Let be an eigenvalue of a second-order elliptic operator defined on an open, sufficiently smooth, bounded domain Ω in ℝⁿ, with Neumann homogeneous boundary conditions on Γ = tial Ω. Let be the corresponding linearly independent (normalized) eigenfunctions...
The regularity of solutions of various dynamical equations (wave, Euler-Bernoulli, Kirchhoff, Schrödinger) in a bounded open domain in , subject to the action of a point control at some point of , is studied. Detailed proofs of the results are contained in the references [8-10].
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...
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.
This note provides sharp regularity results for general, time-independent, second order, hyperbolic equations with non-homogeneous data of Neumann type.
This note provides sharp regularity results for general, time-independent, second order, hyperbolic equations with non-homogeneous data of Neumann type.
We consider the operator on a complex Hilbert space, where is positive self-adjoint and is self-adjoint, and where, moreover, « is comparable to , », in a technical sense. Two applications are given.
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.
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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