Controllability of Parabolic Equations

Rousseau, Jérôme Le; Lebeau, Gilles; Robbiano, Luc

doi:10.1007/978-3-030-88674-5_7

Cited by 75 publications

(1 citation statement)

References 69 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The general case was left as an open problem. It was then noticed by Lebeau, Le Rousseau, Terpolilli and Trelat when c 2 > c 1 and Γ = ∂Ω that the observability holds using a microlocal argument [9]. This result is equivalent to Chapter VI, Theorem 5.1 of [11] under the hypothesis that Ω 2 and Ω are strictly convex.…”

Section: State Of the Artmentioning

confidence: 90%

Sufficient conditions for the controllability of wave equations with a transmission condition at the interface

Gagnon

2023

ESAIM: COCV

View full text Add to dashboard Cite

show abstract

Section: State Of the Artmentioning

confidence: 90%

Sufficient conditions for the controllability of wave equations with a transmission condition at the interface

Gagnon

2023

ESAIM: COCV

View full text Add to dashboard Cite

show abstract

Parabolic equations with dynamic boundary conditions and drift terms

Khoutaibi

Maniar

Mugnolo

et al. 2022

Mathematische Nachrichten

View full text Add to dashboard Cite

show abstract

Carleman estimate for a strongly damped wave equation and applications to an inverse problem

2012

Math Methods in App Sciences

View full text Add to dashboard Cite

In this paper, we establish a Carleman estimate for a strongly damped wave equation in order to solve a coefficient inverse problems of retrieving a stationary potential from a single time-dependent Neumann boundary measurement on a suitable part of the boundary. This coefficient inverse problem is for a strongly damped wave equation. We prove the uniqueness and the local stability results for this inverse problem. The proof of the results relies on Carleman estimate and a certain energy estimates for hyperbolic equation with strongly damped term. Moreover, this method could be used for a similar inverse problem for an integro-differential equation with hyperbolic memory kernel., provided that u 0 , u 1 are given.Many physical phenomena are properly described by the strongly damped wave equation as (1). Such as equations of type (1) can be considered as a class of linear evolution equations governing the motion of a viscoelastic solid (for example, a bar if the space dimension N D 1 and a plate if N D 2) composed of the material of the rate type; see [1][2][3][4]. They can also be seen as field equations governing the longitudinal motion of a viscoelastic bar obeying the simply Voigt model [5]. Mathematical studies on this direct problem have been extensively developed, for example, see [1,2,[6][7][8][9] and the references therein, where the global existence and other properties of solutions are obtained. However, very little work is concerned with the inverse problem for this strongly damped wave equation.The key ingredient we follow here to determine the coefficient relies on the global Carleman estimates. For the first time, the method of Carleman estimates was introduced in the field of inverse problems in the work of Bukhgeim and Klibanov [10], also for some followup publications [11,12] of these authors. A Carleman estimate is an efficient tool not only for the unique continuation, but also for

show abstract

Controllability of Parabolic Equations

Cited by 75 publications

References 69 publications

Sufficient conditions for the controllability of wave equations with a transmission condition at the interface

Sufficient conditions for the controllability of wave equations with a transmission condition at the interface

Parabolic equations with dynamic boundary conditions and drift terms

Carleman estimate for a strongly damped wave equation and applications to an inverse problem

Contact Info

Product

Resources

About