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All issues Volume 28 (2022) ESAIM: COCV, 28 (2022) 63 References
Open Access
Issue
ESAIM: COCV
Volume 28, 2022
Article Number 63
Number of page(s) 29
DOI https://doi.org/10.1051/cocv/2022057
Published online 28 September 2022
  1. M. Badra and T. Takahashi, Maximal regularity for the Stokes system coupled with a wave equation: application to the system of interaction between a viscous incompressible fluid and an elastic wall. J. Evol. Equ. 22 (2022) 71. [CrossRef] [Google Scholar]
  2. M. Badra and T. Takahashi, Feedback stabilization of a fluid-rigid body interaction system. Adv. Differ. Equ. 19 (2014) 1137–1184. [Google Scholar]
  3. M. Badra and T. Takahashi, Feedback stabilization of a simplified 1d fluid-particle system. Ann. Inst. H. Poincaré Anal. Non Linéaire 31 (2014) 369–389. [Google Scholar]
  4. M. Badra and T. Takahashi, Feedback boundary stabilization of 2D fluid-structure interaction systems. Discrete Contin. Dyn. Syst. 37 (2017) 2315–2373. [CrossRef] [MathSciNet] [Google Scholar]
  5. M. Badra and T. Takahashi, Gevrey regularity for a system coupling the Navier-Stokes system with a beam equation. SIAM J. Math. Anal. 51 (2019) 4776–4814. [CrossRef] [MathSciNet] [Google Scholar]
  6. M. Badra and T. Takahashi, Gevrey regularity for a system coupling the Navier-Stokes system with a beam: the non-flat case. Funkcialaj Ekvacioj 65 (2022) 63–109. [CrossRef] [MathSciNet] [Google Scholar]
  7. H. Beirão da Veiga, On the existence of strong solutions to a coupled fluid-structure evolution problem. J. Math. Fluid Mech. 6 (2004) 21–52. [CrossRef] [MathSciNet] [Google Scholar]
  8. M. Bellassoued and J. Le Rousseau, Carleman estimates for elliptic operators with complex coefficients. Part I: Boundary value problems. J. Math. Pures Appl. 104 (2015) 657–728. [CrossRef] [MathSciNet] [Google Scholar]
  9. M. Bellassoued and J. Le Rousseau, Carleman estimates for elliptic operators with complex coefficients. Part II: Transmission problems. J. Math. Pures Appl. 115 (2018) 127–186. [CrossRef] [MathSciNet] [Google Scholar]
  10. M. Boulakia and S. Guerrero, Local null controllability of a fluid-solid interaction problem in dimension 3. J. Eur. Math. Soc. (JEMS) 15 (2013) 825–856. [Google Scholar]
  11. M. Boulakia and A. Osses, Local null controllability of a two-dimensional Fluid-structure interaction problem. ESAIM: COCV 14 (2008) 1–42. [CrossRef] [EDP Sciences] [Google Scholar]
  12. F. Boyer and P. Fabrie, Mathematical tools for the study of the incompressible Navier-Stokes equations and related models. Vol. 183 of Applied Mathematical Sciences. Springer, New York (2013). [CrossRef] [Google Scholar]
  13. R. Buffe, Stabilization of the wave equation with Ventcel boundary condition, J. Math. Pures Appl. 108 (2017) 207–259. [CrossRef] [MathSciNet] [Google Scholar]
  14. R. Buffe and L. Gagnon, Spectral inequality for an Oseen operator in a two dimensional channel (2021), working paper or preprint. [Google Scholar]
  15. S. Čanić, B. Muha and M. Bukač, Fluid-structure interaction in hemodynamics: modeling, analysis, and numerical simulation, in Fluid-structure interaction and biomedical applications, Adv. Math. Fluid Mech. Birkhäuser/Springer, Basel (2014), pp. 79–195. [Google Scholar]
  16. A. Chambolle, B. Desjardins, M.J. Esteban and C. Grandmont, Existence of weak solutions for the unsteady interaction of a viscous fluid with an elastic plate. J. Math. Fluid Mech. 7 (2005) 368–404. [CrossRef] [MathSciNet] [Google Scholar]
  17. F.W. Chaves-Silva and G. Lebeau, Spectral inequality and optimal cost of controllability for the Stokes system. ESAIM: COCV 22 (2016) 1137–1162. [CrossRef] [EDP Sciences] [Google Scholar]
  18. S.P. Chen and R. Triggiani, Proof of extensions of two conjectures on structural damping for elastic systems. Pacific J. Math. 136 (1989) 15–55. [CrossRef] [MathSciNet] [Google Scholar]
  19. N. Cîndea, S. Micu, I. Roventa and M. Tucsnak, Particle supported control of a fluid-particle system. J. Math. Pures Appl. 104 (2015) 311–353. [CrossRef] [MathSciNet] [Google Scholar]
  20. I.A. Djebour, Local null controllability of a fluid-rigid body interaction problem with Navier slip boundary conditions. ESAIM: COCCV 27 (2021) 46. [CrossRef] [EDP Sciences] [Google Scholar]
  21. A. Doubova and E. Fernández-Cara, Some control results for simplified one-dimensional models of fluid-solid interaction. Math. Models Methods Appl. Sci. 15 (2005) 783–824. [CrossRef] [MathSciNet] [Google Scholar]
  22. E. Fernáandez-Cara, S. Guerrero, O.Y. Imanuvilov and J.-P. Puel, Local exact controllability of the Navier-Stokes system. J. Math. Pures Appl. 83 (2004) 1501–1542. [CrossRef] [MathSciNet] [Google Scholar]
  23. C. Grandmont, Existence of weak solutions for the unsteady interaction of a viscous fluid with an elastic plate. SIAM J. Math. Anal. 40 (2008) 716–737. [CrossRef] [MathSciNet] [Google Scholar]
  24. C. Grandmont and M. Hillairet, Existence of global strong solutions to a beam-fluid interaction system. Arch. Ration. Mech. Anal. 220 (2016) 1283–1333. [CrossRef] [MathSciNet] [Google Scholar]
  25. C. Grandmont, M. Hillairet and J. Lequeurre, Existence of local strong solutions to fluid-beam and fluid-rod interaction systems. Ann. Inst. H. Poincare Anal. Non Linéaire 36 (2019) 1105–1149. [CrossRef] [MathSciNet] [Google Scholar]
  26. O. Imanuvilov and T. Takahashi, Exact controllability of a fluid-rigid body system. J. Math. Pures Appl. 87 (2007) 408–437. [CrossRef] [MathSciNet] [Google Scholar]
  27. O.Y. Imanuvilov, On exact controllability for the Navier-Stokes equations, ESAIM: COCV 3 (1998) 97–131. [CrossRef] [EDP Sciences] [Google Scholar]
  28. D. Jerison and G. Lebeau, Nodal sets of sums of eigenfunctions, in Harmonic analysis and partial differential equations (Chicago, IL, 1996), Chicago Lectures in Math., 223–239, Univ. Chicago Press, Chicago, IL (1999). [Google Scholar]
  29. J. Le Rousseau, M. Láeautaud and L. Robbiano, Controllability of a parabolic system with a diffuse interface. J. Eur. Math. Soc. (JEMS) 15 (2013) 1485–1574. [CrossRef] [MathSciNet] [Google Scholar]
  30. J. Le Rousseau, G. Lebeau and L. Robbiano, Elliptic Carleman estimates and applications to stabilization and controllability. Volume I. Dirichlet boundary conditions on Euclidean space. Prog. Nonlinear Differ. Equ. Appl., vol. 97, Cham: Birkhäuser (2021). [Google Scholar]
  31. J. Le Rousseau, G. Lebeau and L. Robbiano, Elliptic Carleman estimates and applications to stabilization and controllability. Volume II. General Boundary Conditions on Riemannian Manifolds. Prog. Nonlinear Differ. Equ. Appl., vol. 97, Birkhäauser, Cham (2022). [Google Scholar]
  32. J. Le Rousseau and N. Lerner, Carleman estimates for anisotropic elliptic operators with jumps at an interface. Anal. PDE 6 (2013) 1601–1648. [CrossRef] [MathSciNet] [Google Scholar]
  33. J. Le Rousseau and L. Robbiano, Carleman estimate for elliptic operators with coefficients with jumps at an interface in arbitrary dimension and application to the null controllability of linear parabolic equations. Arch. Ratl. Mech. Anal. 195 (2010) 953–990. [CrossRef] [Google Scholar]
  34. J. Le Rousseau and L. Robbiano, Local and global Carleman estimates for parabolic operators with coefficients with jumps at interfaces. Invent. Math. 183 (2011) 245–336. [CrossRef] [MathSciNet] [Google Scholar]
  35. M. Láeautaud, Spectral inequalities for non-selfadjoint elliptic operators and application to the null-controllability of parabolic systems. J. Funct. Anal. 258 (2010) 2739–2778. [CrossRef] [MathSciNet] [Google Scholar]
  36. G. Lebeau and L. Robbiano, Contrôle exact de l’áquation de la chaleur. Comm. Partial Differ. Equ. 20 (1995) 335–356. [CrossRef] [Google Scholar]
  37. D. Lengeler, Weak solutions for an incompressible, generalized Newtonian fluid interacting with a linearly elastic Koiter type shell. SIAM J. Math. Anal. 46 (2014) 2614–2649. [CrossRef] [MathSciNet] [Google Scholar]
  38. D. Lengeler and M. Růžička, Weak solutions for an incompressible Newtonian fluid interacting with a Koiter type shell. Arch. Rati. Mech. Anal. 211 (2014) 205–255. [CrossRef] [Google Scholar]
  39. J. Lequeurre, Existence of strong solutions to a fluid-structure system. SIAM J. Math. Anal. 43 (2011) 389–410. [CrossRef] [MathSciNet] [Google Scholar]
  40. Y. Liu, T. Takahashi and M. Tucsnak, Single input controllability of a simplified fluid-structure interaction model. ESAIM: COCV 19 (2013) 20–42. [CrossRef] [EDP Sciences] [Google Scholar]
  41. D. Maity, A. Roy and T. Takahashi, Existence of strong solutions for a system of interaction between a compressible viscous fluid and a wave equation. Nonlinearity 34 (2021) 2659–2687. [CrossRef] [MathSciNet] [Google Scholar]
  42. D. Maity and T. Takahashi, Lp Theory for the Interaction Between the Incompressible Navier—Stokes System and a Damped Plate. J. Math. Fluid Mech. 23 (2021) 103. [CrossRef] [Google Scholar]
  43. D. Maity and T. Takahashi, Existence and uniqueness of strong solutions for the system of interaction between a compressible Navier-Stokes-Fourier fluid and a damped plate equation. Nonlinear Anal. Real World Appl. 59 (2021) Paper No. 103267, 34. [CrossRef] [Google Scholar]
  44. L. Miller, A direct Lebeau-Robbiano strategy for the observability of heat-like semigroups. Discrete Contin. Dyn. Syst. Ser. B 14 (2010) 1465–1485. [Google Scholar]
  45. S. Mitra, Observability and unique continuation of the adjoint of a linearized simplified compressible fluid-structure model in a 2D channel. ESAIM: COCV 27 (2021) Paper No. S18, 51. [CrossRef] [EDP Sciences] [Google Scholar]
  46. B. Muha and S. Čanić, Existence of a weak solution to a nonlinear fluid-structure interaction problem modeling the flow of an incompressible, viscous fluid in a cylinder with deformable walls. Arch. Ratl. Mech. Anal. 207 (2013) 919–968. [CrossRef] [Google Scholar]
  47. B. Muha and S. Čanićc, Existence of a weak solution to a nonlinear Fluid-structure interaction problem modeling the flow of an incompressible, viscous fluid in a cylinder with deformable walls. Arch. Ratl. Mech. Anal. 207 (2013) 919–968. [CrossRef] [Google Scholar]
  48. B. Muha and S. Čanićc, A nonlinear, 3D fluid-structure interaction problem driven by the time-dependent dynamic pressure data: a constructive existence proof. Commun. Inf. Syst. 13 (2013) 357–397. [CrossRef] [MathSciNet] [Google Scholar]
  49. B. Muha and S. Čanićc, Fluid-structure interaction between an incompressible, viscous 3D fluid and an elastic shell with nonlinear Koiter membrane energy. Interfaces Free Bound. 17 (2015) 465–495. [CrossRef] [MathSciNet] [Google Scholar]
  50. A. Quarteroni, M. Tuveri and A. Veneziani, Computational vascular fluid dynamics: problems, models and methods. Comput. Visualizat. Sci. 2 (2000) 163–197. [CrossRef] [Google Scholar]
  51. M. Ramaswamy, A. Roy and T. Takahashi, Remark on the global null controllability for a viscous Burgers-particle system with particle supported control. Appl. Math. Lett. 107 (2020) 106483, 7. [CrossRef] [MathSciNet] [Google Scholar]
  52. J.-P. Raymond, Feedback stabilization of a fluid-structure model. SIAM J. Control Optim. 48 (2010) 5398–5443. [CrossRef] [MathSciNet] [Google Scholar]
  53. L. Robbiano, Cost function and control of solutions of hyperbolic equations. Asymptotic Anal. 10 (1995) 95–115. [CrossRef] [MathSciNet] [Google Scholar]
  54. A. Roy and T. Takahashi, Local null controllability of a rigid body moving into a Boussinesq flow. Math. Control Relat. Fields 9 (2019) 793–836. [Google Scholar]
  55. A. Roy and T. Takahashi, Stabilization of a rigid body moving in a compressible viscous fluid. J. Evol. Equ. 21 (2021) 167–200. [CrossRef] [MathSciNet] [Google Scholar]
  56. D.L. Russell, A unified boundary controllability theory for hyperbolic and parabolic partial differential equations. Studies in Appl. Math. 52 (1973) 189–211. [CrossRef] [MathSciNet] [Google Scholar]
  57. T. Takahashi, M. Tucsnak and G. Weiss, Stabilization of a fluid-rigid body system. J. Differ. Equ. 259 (2015) 6459–6493. [Google Scholar]
  58. S. Trifunovićc and Y. Wang, Weak solution to the incompressible viscous fluid and a thermoelastic plate interaction problem in 3D. Acta Math. Sci. Ser. B (Engl. Ed.) 41 (2021) 19–38. [MathSciNet] [Google Scholar]
  59. S. Trifunovićc and Y.-G. Wang, Existence of a weak solution to the Fluid-structure interaction problem in 3D. J. Differ. Equ. 268 (2020) 1495–1531. [CrossRef] [Google Scholar]
  60. M. Tucsnak and G. Weiss, Observation and control for operator semigroups, Birkhäuser Advanced Texts: Basler Lehrbucher. [Birkhäuser Advanced Texts: Basel Textbooks], Birkhäuser Verlag, Basel (2009). [Google Scholar]

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