Free Access
Issue
ESAIM: COCV
Volume 26, 2020
Article Number 18
Number of page(s) 34
DOI https://doi.org/10.1051/cocv/2019066
Published online 19 February 2020
  1. F. Alabau-Boussouira, P. Cannarsa and G. Fragnelli, Carleman estimates for degenerate parabolic operators with applications to null controllability. J. Evol. Equ. 6 (2006) 161–204. [CrossRef] [MathSciNet] [Google Scholar]
  2. F. Alabau-Boussouira, P. Cannarsa and G. Leugering, Control and stabilization of degenerate wave equations. SIAM J. Control Optim. 6 (2017) 161–204. [Google Scholar]
  3. P. Baldi, G. Floridia and E. Haus, Exact controllability for quasi-linear perturbations of KdV. Anal. PDE 10 (2017) 281–322. [CrossRef] [Google Scholar]
  4. J.M. Ball, J.E. Marsden, M. Slemrod, Controllability for distributed bilinear systems, SIAM J. Control Optim. 20, no. 4, (1982) 555–587. [Google Scholar]
  5. K. Beauchard and C. Laurent, Local controllability of 1D linear and nonlinear Schrödinger equations with bilinear control. J. Math. Pures Appl. 94 (2010) 520–554. [CrossRef] [Google Scholar]
  6. A. Bensoussan, G. Da Prato, G. Delfour and S.K. Mitter, Representation and control of infinite dimensional systems. Syst. Control Found. Appl. 1 (1992). [Google Scholar]
  7. M.I. Budyko, The effect of solar radiation variations on the climate of the earth. Tellus 21 (1969) 611–619. [CrossRef] [Google Scholar]
  8. M. Campiti, G. Metafune and D. Pallara, Degenerate self-adjoint evolution equations on the unit interval. Semigroup Forum 57 (1998) 1–36. [CrossRef] [MathSciNet] [Google Scholar]
  9. P. Cannarsa and G. Floridia, Approximate controllability for linear degenerate parabolic problems with bilinear control. Proc. Evolution Equations and Materials with Memory 2010, Casa Editrice Università La Sapienza Roma (2011) 19–36. [Google Scholar]
  10. P. Cannarsa and G. Floridia, Approximate multiplicative controllability for degenerate parabolic problems with Robin boundary conditions. Commun. Appl. Ind. Math. 2 (2011) 1–16. [Google Scholar]
  11. P. Cannarsa, G. Floridia, F. Gölgeleyen and M. Yamamoto, Inverse coefficient problems for a transport equation by local Carleman estimate. Inverse Probl. 35 (2019) https://doi.org/10.1088/1361-6420/ab1c69. [CrossRef] [Google Scholar]
  12. P. Cannarsa, G. Floridia and A.Y. Khapalov, Multiplicative controllability for semilinear reaction-diffusion equations with finitely many changes of sign. J. Math. Pures Appl. 108 (2017) 425–458. [CrossRef] [Google Scholar]
  13. P. Cannarsa, G. Floridia and M. Yamamoto, Observability inequalities for transport equations through Carleman estimates. Springer INdAM series. Vol. 32 of Trends in Control Theory and Partial Differential Equations, edited by F. Alabau-Boussouira, F. Ancona, A. Porretta, C. Sinestrari (2019) 69–87 https://doi.org/10.1007/978-3-030-17949-6_4. [CrossRef] [Google Scholar]
  14. P. Cannarsa, P. Martinez and J. Vancostenoble, Persistent regional contrallability for a class of degenerate parabolic equations. Commun. Pure Appl. Anal. 3 (2004) 607–635. [CrossRef] [MathSciNet] [Google Scholar]
  15. P. Cannarsa, P. Martinez and J. Vancostenoble, Carleman estimates for a class of degenerate parabolic operators. SIAM J. Control Optim. 47 (2008) 1–19. [Google Scholar]
  16. P. Cannarsa, P. Martinez and J. Vancostenoble, Global Carleman estimates for degenerate parabolic operators with applications. Memoirs AMS 239 (2016) 1–209. [CrossRef] [Google Scholar]
  17. P. Cannarsa, P. Martinez and J. Vancostenoble, The cost of controlling weakly degenerate parabolic equations by boundary controls. Math. Control Relat. Fields 2 (2017) 171–211. [CrossRef] [Google Scholar]
  18. P. Cannarsa, J. Tort and M. Yamamoto, Determination of source terms in a degenerate parabolic equation. Inverse Probl. 26 (2010). [CrossRef] [Google Scholar]
  19. M.M. Cavalcanti, E. Fernández-Cara and A.L. Ferreira, Null controllability of some nonlinear degenerate 1D parabolic equations. J. Franklin Inst. 354 (2017) 6405–6421. [CrossRef] [Google Scholar]
  20. J.-M. Coron, L. Gagnon and M. Morancey, Rapid stabilization of a linearized bilinear 1–D Schrödinger equation. J. Math. Pures Appl. 115 (2018) 24–73. [CrossRef] [Google Scholar]
  21. J.I. Diaz, Mathematical analysis of some diffusive energy balance models in climatology. Math. Clim. Environ. (1993) 28–56. [Google Scholar]
  22. J.I. Diaz, On the controllability of some simple climate models, Environ. Econ. Math. Models (1994) 29–44. [Google Scholar]
  23. I. El Harraki and A. Boutoulout, Controllability of the wave equation via multiplicative controls. IMA J. Math. Control Inf . (2016). [Google Scholar]
  24. C.L. Epstein and R. Mazzeo, Degenerate diffusion operators arising in population biology, Ann. Math. Stud. (2013). [Google Scholar]
  25. C. Fabre, J.P. Puel and E. Zuazua, Approximate controllability for the semilinear heat equation. Proc. Roy. Soc. Edinburgh 125A (1995) 31–61. [CrossRef] [MathSciNet] [Google Scholar]
  26. H.O. Fattorini and D.L. Russell, Exact controllability theorems for linear parabolic equations in one space dimension. Arch. Rational Mech. Anal. 43 (1971) 272–292. [CrossRef] [Google Scholar]
  27. E. Fernandez-Cara and E. Zuazua, Controllability for blowing up semilinear parabolic equations. C. R. Acad. Sci. Paris Ser. I Math. 330 (2000) 199–204. [CrossRef] [Google Scholar]
  28. G. Fichera, On a degenerate evolution problem, Partial differential equations with real analysis, edited by H. Begeher, A. Jeffrey, Pitman (1992) 1–28. [Google Scholar]
  29. G. Floridia, Approximate controllability for nonlinear degenerate parabolic problems with bilinear control, J. Differ. Equ. 9 (2014) 3382–3422. [Google Scholar]
  30. G. Floridia, Well-posedness for a class of nonlinear degenerate parabolic equations, Dyn. Syst. Differ. Equ. Appl. AIMS Proceedings (2015) 455–463. [Google Scholar]
  31. G. Floridia and M.A. Ragusa, Differentiability and partial Hölder continuity of solutions of nonlinear elliptic systems. J. Convex Anal. 19 (2012) 63–90. [Google Scholar]
  32. G. Fragnelli, G.R. Goldstein, J. Goldstein, R.M. Mininni and S. Romanelli, Generalized Wentzell boundary conditions for second order operators with interior degeneracy. Discr. Continu. Dyn. Syst. Ser. S 9 (2016) 697–715. [CrossRef] [Google Scholar]
  33. A.Y. Khapalov, Controllability of partial differential equations governed by multiplicative controls. Vol. 1995 of Lecture Series in Mathematics, Springer (2010). [CrossRef] [Google Scholar]
  34. A.Y. Khapalov, P. Cannarsa, F.S. Priuli and G. Floridia, Wellposedness of a 2-D and 3-D swimming models in the incompressible fluid governed by Navier-Stokes equation. J. Math. Anal. Appl. 429 (2015) 1059–1085. [Google Scholar]
  35. O.H. Ladyzhenskaya, V.A. Solonikov and N.N. Ural’ceva, Linear and Quasi-linear Equations of Parabolic Type. AMS, Providence, Rhode Island (1968), pp. 667. [Google Scholar]
  36. P. Martinez, J.P. Raymond and J. Vancostenoble, Regional null controllability of a linearized Crocco-type equation. SIAM J. Control Optim. 42 (2003) 709–728. [Google Scholar]
  37. H. Matano, Nonincrease of the lap-number of a solution for a one-dimensional semilinear parabolic equation. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 29 (1982) 401–441. [Google Scholar]
  38. O.A. Oleinik and E.V. Radkevich, Second order equations with nonnegative characteristic form. Appl. Math. Sci. (1983). [Google Scholar]
  39. M. Ouzahra, A. Tsouli and A. Boutoulout, Exact controllability of the heat equation with bilinear control. Math. Methods Appl. Sci. 38 (2015) 5074–5084. [Google Scholar]
  40. D. Pighin and E. Zuazua, Controllability under positivity constraints of multi-d wave equations. Preprint arXiv:1804.02151 (2018). [Google Scholar]
  41. C. Pignotti and E. Trélat, Convergence to consensus of the general finite-dimensional Cucker-Smale model with time-varying delays. Preprint arXiv:1707.05020v2 (2017). [Google Scholar]
  42. C. Pouchol, E. Trélat and E. Zuazua, Phase portrait control for 1D monostable and bistable reaction-diffusion equations. Preprint arXiv:1805.10786 (2018). [Google Scholar]
  43. W.D. Sellers, A climate model based on the energy balance of the earth-atmosphere system. J. Appl. Meteor. 8 (1969) 392–400. [CrossRef] [Google Scholar]
  44. E. Trélat, J. Zhu and E. Zuazua, Allee optimal control of a system in ecology. Math. Models Methods Appl. Sci. 28 (2018) 1665–1697. [Google Scholar]

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