Open Access
Volume 28, 2022
Article Number 73
Number of page(s) 19
Published online 22 December 2022
  1. M. Ashyraliyev, A note on the stability of the integral-differential equation of the hyperbolic type in a Hilbert space. Numer. Func. Anal. Optim. 29 (2008) 750–769. [CrossRef] [Google Scholar]
  2. V. Barbu and M. Lannelli, Controllability of the heat equation with memory. Differ. Integr. Equ. 13 (2000) 1393–1412. [Google Scholar]
  3. A.J.V. Brandao, E. Fernandez-Cara, P.M.D. Magalhaes and M.A. Rojas-Medar, Theoretical analysis and control results for the Fitzhugh-Nagumo equation. Electr. J. Differ. Equ. 2008 (2008) 1–20. [Google Scholar]
  4. F.W. Chaves-Silva, X. Zhang and E. Zuazua, Controllability of evolution equations with memory. SIAM J. Control Optim. 55 (2017) 2437–2459. [CrossRef] [MathSciNet] [Google Scholar]
  5. B.D. Coleman and M.E. Gurtin, Equipresence and constitutive equations for rigid heat conductors. Z. Angew. Math. Phys. 18 (1967) 199–208. [CrossRef] [MathSciNet] [Google Scholar]
  6. R.F. Curtain and A.J. Pritchard, Infinite dimensional linear systems theory. Lecture Notes in Control and Information Sciences, Springer-Verlag, Berlin (1978). [CrossRef] [Google Scholar]
  7. M. Grasselli and A. Lorenzi, Abstract nonlinear Volterra integrodifferential equations with nonsmooth kernels. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 2 (1991) 43–53. [MathSciNet] [Google Scholar]
  8. S. Guerrero and O.Y. Imanuvilov, Remarks on non controllability of the heat equation with memory. ESAIM: COCV 19 (2013) 288–300. [CrossRef] [EDP Sciences] [Google Scholar]
  9. A. Halanay and L. Pandolfi, Approximate controllability and lack of controllability to zero of the heat equation with memory. J. Math. Anal. Appl. 425 (2015) 194–211. [CrossRef] [MathSciNet] [Google Scholar]
  10. S. Lang, Real and Functional Analysis. Springer-Verlag, New York (1993). [Google Scholar]
  11. R.K. Miller, An integro-differential equation for rigid heat conductors with memory. J. Math. Anal. Appl. 66 (1978) 313–332. [CrossRef] [MathSciNet] [Google Scholar]
  12. G.S. Wang, L.J. Wang, Y.S. Xu and Y.B. Zhang, Time Optimal Control of Evolution Equations. Birkhauser, Cham (2018). [Google Scholar]
  13. G.S. Wang and Y.S. Xu, Equivalence of three different kinds of optimal control problems for heat equations and its applications. SIAM J. Control Optim. 51 (2013) 848–880. [CrossRef] [MathSciNet] [Google Scholar]
  14. G.S. Wang, Y.B. Zhang and E. Zuazua, Flow decomposition for heat equations with memory. J. Math. Pures Appl. 158 (2022) 183–215. [CrossRef] [MathSciNet] [Google Scholar]
  15. G.S. Wang, Y.B. Zhang and E. Zuazua, Observability for heat equations with memory. Preprint arXiv:2101.10615v2. [Google Scholar]
  16. L.J. Wang and X.X. Zhou, Minimal time control problem of a linear heat equation with memory. Syst. Control Lett. 157 (2021) Paper No. 105052, 7 pp. [Google Scholar]
  17. Z.Q. Wu, J.X. Yin and C.P. Wang, Elliptic and Parabolic Equations. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ (2006). [Google Scholar]
  18. J.M. Yong and X. Zhang, Heat equation with memory in anisotropic and non-homogeneous media. Acta Math. Sin. (Engl. Ser.) 27 (2011) 219–254. [CrossRef] [MathSciNet] [Google Scholar]
  19. X.X. Zhou, Integral-type approximate controllability of linear parabolic integro-differential equations. Systems Control Lett. 105 (2017) 44–47. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.