In this paper we consider a viscoelastic three dimensional body (of Maxwell–Boltzmann type) controlled on (part of) the boundary. We assume that the material is isotropic and homogeneous. If the body is elastic (
Accepté le :
DOI : 10.1051/cocv/2016068
Mots-clés : Controllability, systems with persistent memory, viscoelasticity
@article{COCV_2017__23_4_1649_0, author = {Pandolfi, L.}, title = {Controllability of isotropic viscoelastic bodies of {Maxwell{\textendash}Boltzmann} type}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {1649--1666}, publisher = {EDP-Sciences}, volume = {23}, number = {4}, year = {2017}, doi = {10.1051/cocv/2016068}, zbl = {1398.93048}, mrnumber = {3716936}, language = {en}, url = {https://www.numdam.org/articles/10.1051/cocv/2016068/} }
TY - JOUR AU - Pandolfi, L. TI - Controllability of isotropic viscoelastic bodies of Maxwell–Boltzmann type JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2017 SP - 1649 EP - 1666 VL - 23 IS - 4 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2016068/ DO - 10.1051/cocv/2016068 LA - en ID - COCV_2017__23_4_1649_0 ER -
%0 Journal Article %A Pandolfi, L. %T Controllability of isotropic viscoelastic bodies of Maxwell–Boltzmann type %J ESAIM: Control, Optimisation and Calculus of Variations %D 2017 %P 1649-1666 %V 23 %N 4 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/cocv/2016068/ %R 10.1051/cocv/2016068 %G en %F COCV_2017__23_4_1649_0
Pandolfi, L. Controllability of isotropic viscoelastic bodies of Maxwell–Boltzmann type. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 4, pp. 1649-1666. doi : 10.1051/cocv/2016068. https://www.numdam.org/articles/10.1051/cocv/2016068/
S. Agmon, Lectures on elliptic boundary value problems. D. Van Nostrand Co., Princeton (1965). | MR | Zbl
Controllability of a nonhomogeneous string and ring under time dependent tension. MMNP 5 (2010) 4–31. | MR | Zbl
, and ,Recent progresses in the boundary control method. Inv. Probl. 23 (2007) R1–R67. | DOI | MR | Zbl
,The dynamical Lamé system: Regularity of solutions, boundary controllability and boundary data continuation. ESAIM: COCV 8 (2002) 143–167. | Numdam | MR | Zbl
and ,Universal inequalities for eigenvalues of a system of elliptic equations. Proc. R. Soc. Edinb. Sec. A 139 (2009) 273–285. | DOI | MR | Zbl
and ,Boundary value problems for systems of elastostatics in Lipschitz domains. Duke Math. J. 57 (1988) 795–818. | DOI | MR | Zbl
, and ,An inverse source problem for the Lamé system with variable coefficients. Appl. Anal. 84 (2005) 357–375. | DOI | MR | Zbl
, and ,Identifying a spatial body force in linear elastodynamics via traction measurements. SIAM J. Control Optim. 36 (1998) 1190–1206. | DOI | MR | Zbl
and ,Erratum for “Upper and lower bounds for normal derivatives of Dirichlet eigenfunctions”. Math. Res. Lett. 17 (2010) 793–794. | DOI | MR | Zbl
and ,I. Lasiecka and R. Triggiani, Control theory for partial differential equations: continuous and approximation theories. I. Abstract parabolic systems. Vol. 74 of Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge (2000). | MR | Zbl
J.-L. Lions, Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués. Tome 1. Vol. 8 of Recherches en Mathématiques Appliquées. Masson, Paris (1988). | MR | Zbl
Boundary controllability and observability of a viscoelastic string. SIAM J. Control Optim. 50 (2012) 820–844. | DOI | MR | Zbl
, and ,H. Kolsky, Stress waves in solids. Dover publ., New York (1963). | Zbl
The controllability of the Gurtin-Pipkin equation: a cosine operator approach. Appl. Math. Optim. 52 (2005) 143–165 (a correction in Appl. Math. Optim. 64 (2011) 467–468). | DOI | MR | Zbl
,Riesz systems and controllability of heat equations with memory. Int. Equ. Oper. Theory 64 (2009) 429–453. | DOI | MR | Zbl
,Riesz systems and moment method in the study of heat equations with memory in one space dimension. Discrete Contin. Dyn. Syst. Ser. B. 14 (2010) 1487–1510. | MR | Zbl
,Sharp control time for viscoelastic bodies. J. Int. Equ. Appl. 27 (2015) 103–136. | MR | Zbl
,L. Pandolfi, Distributed systems with persistent memory. Control and moment problems. Springer Briefs in Electrical and Computer Engineering. Control, Automation and Robotics. Springer, Cham (2014). | MR | Zbl
L. Pandolfi, Cosine operator and controllability of the wave equation with memory revisited. Preprint (2016). | arXiv
L. Pandolfi, Controllability of a viscoelastic plate using one boundary control in displacement or bending. Preprint (2016). | arXiv | MR
Propriétés asymptotique des fonctions fondamentales du problème des vibrations dans un corps élastique. Ark. Mat. Astron. Fysik 26 (1939) 19. | JFM | MR
,J.J Telega and W.R. Bielski, Exact controllability of anisotropic elastic bodies, in Modelling and optimization of distributed parameter systems, Warsaw, 1995. Chapman & Hall, New York (1996) 254–262. | MR | Zbl
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