Free Access
Volume 25, 2019
Article Number 60
Number of page(s) 26
Published online 25 October 2019
  1. J.L. Boldrini, A. Doubova, E. Fernández-Cara and M. González-Burgos, Some controllability results for linear viscoelastic fluids. SIAM J. Control Optim. 50 (2012) 900–924. [CrossRef] [Google Scholar]
  2. F.W. Chaves-Silva, X. Zhang and E. Zuazua, Controllability of evolution equations with memory. SIAM J. Control Optim. 55 (2017) 2437–2459. [CrossRef] [Google Scholar]
  3. S. Chowdhury, D. Mitra, M. Ramaswamy and M. Renardy, Approximate controllability results for linear viscoelastic flows. J. Math. Fluid Mech. 19 (2017) 529–549. [CrossRef] [Google Scholar]
  4. A. Doubova and E. Fernández-Cara, On the control of viscoelastic Jeffreys fluids. Syst. Cont. Lett. 61 (2012) 573–579. [CrossRef] [Google Scholar]
  5. A. Doubova, E. Fernández-Cara and M. González-Burgos, Controllability results for linear viscoelastic fluids of the Maxwell and Jeffreys kinds. C. R. Acad. Sci. Paris Sér. I Math. 331 (2000) 537–542. [CrossRef] [Google Scholar]
  6. Edited by Yu.V. Egorov and M.A. Shubin, Microlocal analysis. Springer Verlag Berlin, Heidelberg (1993) 1–147. [Google Scholar]
  7. V. Girault and P.A. Raviart, Finite element methods for Navier-Stokes equations, Theory and algorithms, in vol. 5 of Springer Series in Computational Mathematics. Springer-Verlag, Berlin (1986). [CrossRef] [Google Scholar]
  8. S. Guerrero and O.Yu. Imanuvilov, Remarks on non-controllability of the heat equation with memory. ESAIM: COCV 19 (2013) 288–300. [CrossRef] [EDP Sciences] [Google Scholar]
  9. L. Hörmander, The Analysis of Linear Partial Differential Operators. I. Distribution theory and Fourier analysis. Distribution theory and Fourier analysis. In Springer Study Edition., 2nd edn. Springer-Verlag, Berlin (2003). [Google Scholar]
  10. I. Lasiecka, Controllability of a viscoelastic Kirchhoff plate. In Control and Estimation of Distributed Parameter Systems (Vorau, 1988). Vol. 91 of Int. Ser. Numer. Math.. Birkhäuser, Basel (1989) 237–247. [Google Scholar]
  11. G. Leugering, Exact controllability in viscoelasticity of fading memory type. Appl. Anal. 18 (1984) 221–243. [CrossRef] [Google Scholar]
  12. G. Leugering, Exact boundary controllability of an integro-differential equation. Appl. Math. Optim. 15 (1987) 223–250. [CrossRef] [Google Scholar]
  13. G. Leugering, Time optimal boundary controllability of a simple linear viscoelastic liquid. Math. Methods Appl. Sci. 9 (1987) 413–430. [CrossRef] [Google Scholar]
  14. W.J. Liu and G.H. Williams, Partial exact controllability for the linear thermo-viscoelastic model. Electr. J. Differ. Equ. 17 (1998) 11. [Google Scholar]
  15. Q. Lu, X. Zhang and E. Zuazua, Null controllability for wave equations with memory. J. Math. Pures Appl. 108 (2017) 500–531. [CrossRef] [Google Scholar]
  16. D. Mitra, M. Ramaswamy and M. Renardy, Approximate controllability results for viscoelastic flows with infinitely many relaxation modes. J. Differ. Equ. 264 (2018) 575–603. [CrossRef] [Google Scholar]
  17. M. Renardy, Are viscoelastic flows under control or out of control? Syst. Cont. Lett. 54 (2005) 1183–1193. [CrossRef] [Google Scholar]
  18. M. Renardy, Shear flow of viscoelastic fluids as a control problem. J. Non-Newtonian Fluid Mech. 131 (2005) 59–63. [CrossRef] [Google Scholar]
  19. M. Renardy, On control of shear flow of an upper convected Maxwell fluid. Z. Angew. Math. Mech. 87 (2007) 213–218. [CrossRef] [Google Scholar]
  20. M. Renardy, Controllability of viscoelastic stresses for nonlinear Maxwell models. J. Non-Newtonian Fluid Mech. 156 (2009) 70–74. [CrossRef] [Google Scholar]
  21. M. Renardy, A note on a class of observability problems for PDEs. Syst. Control Lett. 58 (2009) 183–187. [CrossRef] [MathSciNet] [Google Scholar]
  22. M. Renardy, W.J. Hrusa and J.A. Nohel, Mathematical Problems in Viscoelasticity. Longman Scientific and Technical, Harlow, Essex (1987). [Google Scholar]
  23. E. Savelev and M. Renardy, Control of homogeneous shear flow of multimode Maxwell fluids. J. Non-Newtonian Fluid Mech. 165 (2010) 136–142. [CrossRef] [Google Scholar]
  24. Q. Tao and H. Gao, On the null controllability of the heat equation with memory. J. Math. Anal. Appl. 440 (2016) 1–13. [CrossRef] [Google Scholar]

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