Reachability of nonnegative equilibrium states  for the semilinear vibrating string by varying its axial load and the gain of damping

Alexander Y. Khapalov

Displaying similar documents to “Reachability of nonnegative equilibrium states for the semilinear vibrating string by varying its axial load and the gain of damping”

Controllability of a quantum particle in a 1D variable domain

Karine Beauchard (2008)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We consider a quantum particle in a 1D infinite square potential well with variable length. It is a nonlinear control system in which the state is the wave function $φ$ of the particle and the control is the length $l (t)$ of the potential well. We prove the following controllability result : given $φ_{0}$ close enough to an eigenstate corresponding to the length $l = 1$ and $φ_{f}$ close enough to another eigenstate corresponding to the length $l = 1$ , there exists a continuous function $l : [0, T] \to ℝ_{+}^{*}$ with $T > 0$ , such that $l (0) = 1$ and $l (T) = 1$ ,...

On the controllability and stabilization of the linearized Benjamin-Ono equation

Felipe Linares, Jaime H. Ortega (2005)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

In this work we are interested in the study of controllability and stabilization of the linearized Benjamin-Ono equation with periodic boundary conditions, which is a generic model for the study of weakly nonlinear waves with nonlocal dispersion. It is well known that the Benjamin-Ono equation has infinite number of conserved quantities, thus we consider only controls acting in the equation such that the volume of the solution is conserved. We study also the stabilization with a feedback...

Global non-negative controllability of the semilinear parabolic equation governed by bilinear control

Alexander Y. Khapalov (2002)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We study the global approximate controllability of the one dimensional semilinear convection-diffusion-reaction equation governed in a bounded domain via the coefficient (bilinear control) in the additive reaction term. Clearly, even in the linear case, due to the maximum principle, such system is not globally or locally controllable in any reasonable linear space. It is also well known that for the superlinear terms admitting a power growth at infinity the global approximate controllability...

Interior point control and observation for the wave equation.

Khapalov, A.Y. (1996)

Abstract and Applied Analysis

Similarity:

Approximate controllability for a system of Schrödinger equations modeling a single trapped ion

Sylvain Ervedoza, Jean-Pierre Puel (2009)

Annales de l'I.H.P. Analyse non linéaire

Similarity:

Null controllability of degenerate parabolic equations of Grushin and Kolmogorov type

Karine Beauchard (2011-2012)

Séminaire Laurent Schwartz — EDP et applications

Similarity:

The goal of this note is to present the results of the references [5] and [4]. We study the null controllability of the parabolic equations associated with the Grushin-type operator $\partial_{x}^{2} + {| x |}^{2 γ} \partial_{y}^{2}$ ( $γ > 0$ ) in the rectangle $(x, y) \in (- 1, 1) \times (0, 1)$ or with the Kolmogorov-type operator $v^{γ} \partial_{x} f + \partial_{v}^{2} f$ ( $γ \in {1, 2}$ ) in the rectangle $(x, v) \in 𝕋 \times (- 1, 1)$ , under an additive control supported in an open subset $ω$ of the space domain. We prove that the Grushin-type...