Volume 27, 2021
Special issue in honor of Enrique Zuazua's 60th birthday
Article Number 70
Number of page(s) 21
Published online 02 July 2021
  1. D. Allonsius and F. Boyer, Boundary null-controllability of semi-discrete coupled parabolic systems in some multi-dimensional geometries. Math. Control Relat. Fields 10 (2020) 217–256. [Google Scholar]
  2. F. Ammar-Khodja, A. Benabdallah, C. Dupaix and M. González-Burgos, A Kalman rank condition for the localized distributed controllability of a class of linear parabolic systems. J. Evol. Equ. 9 (2009) 267–291. [Google Scholar]
  3. F. Ammar-Khodja, A. Benabdallah, M. González-Burgos and L. De Teresa Recent results on the controllability of linear coupled parabolic problems: a survey. Math. Control Relat. Fields 1 (2011) 267–306. [CrossRef] [MathSciNet] [Google Scholar]
  4. H. Antil, U. Biccari, R. Ponce, M. Warma and S. Zamorano, Controllability properties from the exterior under positivity constraints for a 1-d fractional heat equation. Preprint arXiv:1910.14529 (2019). [Google Scholar]
  5. A. Benabdallah, F. Boyer, M. González-Burgos and G. Olive, Sharp estimates of the one-dimensional boundary control cost for parabolic systems and application to the N-dimensional boundary null controllability in cylindrical domains. SIAM J. Control Optim. 52 (2014) 2970–3001. [Google Scholar]
  6. A. Berman and R.J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Classics in Applied Mathematics. Society for Industrial and Applied Mathematics (1994). [Google Scholar]
  7. U. Biccari, M. Warma and E. Zuazua, Controllability of the one-dimensional fractional heat equation under positivity constraints. Commun. Pure Appl. Anal. 19 (2020) 1949–1978. [Google Scholar]
  8. F. Boyer, On the penalised HUM approach and its applications to the numerical approximation of null-controls for parabolic problems. ESAIM: Proc. 41 (2013) 15–58. [Google Scholar]
  9. C. Dupaix, F. Ammar Khodja, A. Benabdalah and M. Gonzalez-Burgos, A generalization of the Kalman rank condition for time-dependent coupled linear parabolic systems. Diff. Equ. Appl. 1 (2009) 427–457. [Google Scholar]
  10. E. Fernández-Cara and E. Zuazua, Null and approximate controllability for weakly blowing up semilinear heat equations. Ann. l’Institut Henri Poincaré Analyse non linéaire 17 (2000) 583–616. [Google Scholar]
  11. 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. Univ. Chicago Press, Chicago, IL (1999) 223–239. [Google Scholar]
  12. O.A. Ladyzhenskaia, V.A. Solonnikov and N.N. Ural’tseva, Vol. 23 of Linear and quasi-linear equations of parabolic type. American Mathematical Soc. (1988). [Google Scholar]
  13. K. Le Balc’h Global null-controllability and nonnegative-controllability of slightly superlinear heat equations. J. Math. Pures Appl. 135 (2020) 103–139. [Google Scholar]
  14. G. Lebeau and E. Zuazua, Null-controllability of a system of linear thermoelasticity. Arch. Ratl. Mech. Anal. 141 (1998) 297–329. [Google Scholar]
  15. P. Lissy and E. Zuazua, Internal observability for coupled systems of linear partial differential equations. SIAM J. Control Optim. 57 (2019) 832–853. [Google Scholar]
  16. J. Lohéac, E. Trélat and E. Zuazua, Minimal controllability time for the heat equation under unilateral state or control constraints. Math. Models Methods Appl. Sci. 27 (2017) 1587–1644. [Google Scholar]
  17. J. Lohéac, E. Trélat and E. Zuazua, Minimal controllability time for finite-dimensional control systems under state constraints. Automatica 96 (2018) 380–392. [Google Scholar]
  18. J. Lohéac, E. Trélat and E. Zuazua, Nonnegative control of finite-dimensional linear systems. Ann. l’Institut Henri Poincaré C, Analyse non linéaire (2020). [Google Scholar]
  19. D. Maity, M. Tucsnak and E. Zuazua, Controllability and positivity constraints in population dynamics with age structuring and diffusion. J. Math. Pures Appl. 129 (2019) 153–179. [Google Scholar]
  20. I. Mazari and D. Ruiz-Balet, Constrained control of bistable reaction-diffusion equations: Gene-flow and spatially heterogeneous models. Preprint arXiv:2005.09236 (2020). [Google Scholar]
  21. L. Miller, A direct Lebeau-Robbiano strategy for the observability of heat-like semigroups. Discrete Contin. Dyn. Syst. Ser. B 14 (2010) 1465–1485. [CrossRef] [MathSciNet] [Google Scholar]
  22. M.R. Nuñez-Chávez, Controllability under positive constraints for quasilinear parabolic PDEs. Preprint arXiv:1912.01486 (2019). [Google Scholar]
  23. M. Pierre, Global existence in reaction-diffusion systems with control of mass: a survey. Milan J. Math. 78 (2010) 417–455. [CrossRef] [Google Scholar]
  24. D. Pighin and E. Zuazua, Controllability under positivity constraints of semilinear heat equations. Math. Control Related Fields 8 (2018) 935–964. [Google Scholar]
  25. D. Pighin and E. Zuazua, Controllability under positivity constraints of multi-d wave equations, in Trends in Control Theory and Partial Differential Equations. Springer (2019) 195–232. [Google Scholar]
  26. D. Ruiz-Balet and E. Zuazua, Control under constraints for multi-dimensional reaction-diffusion monostable and bistable equations. J. Math. Pures Appl. 143 (2020) 345–375. [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.