PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

Controllability of degenerate and singular parabolic problems: the double strong case with Neumann boundary conditionsControllability of degenerate and singular parabolic problems: the double strong case with Neumann boundary conditions

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We prove a null controllability result for a parabolic problem with Neumann boundary conditions. We consider non smooth coefficients in presence of a strongly singular potential and a strongly degenerate coefficient, both vanishing at an interior point. This paper concludes the study of the Neumann case.
Rocznik
Strony
207--225
Opis fizyczny
Bibliogr. 29 poz.
Twórcy
  • Dipartimento di Matematica Universita di Bari "Aldo Moro" Via E. Orabona 4, 70125 Bari, Italy
  • Tuscia University Department of Ecology and Biology Largo del Universita, 01100 Viterbo, Italy
Bibliografia
  • [1] F. Alabau-Boussouira, P. Cannarsa, G Fragnelli, Carleman estimates for degenerate parabolic operators with applications to null controllability, J. Evol. Eqs 6 (2006), 161-204.
  • [2] K. Beauchard, P. Cannarsa, R. Guglielmi, Null controllability of Grushin-type operators in dimension two, J. Eur. Math. Soc. (JEMS) 16 (2014), 67-101.
  • [3] I. Boutaayamou, G. Fragnelli, L. Maniar, Lipschitz stability for linear cascade parabolic systems with interior degeneracy, Electron. J. Diff. Equ. 2014 (2014), 1-26.
  • [4] I. Boutaayamou, G. Fragnelli, L. Maniar, Carleman estimates for parabolic equations with interior degeneracy and Neumann boundary conditions, J. Anal. Math. 135 (2018), 1-35.
  • [5] P. Cannarsa, G. Fragnelli, D. Rocchetti, Null controllability of degenerate parabolic operators with drift, Netw. Heterog. Media 2 (2007), 693-713.
  • [6] P. Cannarsa, G. Fragnelli, D. Rocchetti, Controllability results for a class of one-dimensional degenerate parabolic problems in nondivergence form, J. Evol. Equ. 8 (2008), 583-616.
  • [7] P. Cannarsa, P. Martinez, J. Vancostenoble, Null controllability of the degenerate heat equations, Adv. Differential Equations 10 (2005), 153-190.
  • [8] P. Cannarsa, P. Martinez, J. Vancostenoble, Carleman estimates for a class of degenerate parabolic operators, SIAM J. Control Optim. 47 (2008), 1-19.
  • [9] S. Ervedoza, Null Controllability for a singular heat equation: Garleman estimates and Hardy inequalities, Comm. Partial Differential Equations 33 (2008), 1996-2019.
  • [10] G. Floridia, Approximate controllability for nonlinear degenerate parabolic problems with bilinear control, J. Differential Equations 257 (2014), 3382-3422.
  • [11] M. Fotouhi, L. Salimi, Null controllability of degenerate/singular parabolic equations, J. Dyn. Control Syst. 18 (2012), 573-602.
  • [12] M. Fotouhi, L. Salimi, Controllability results for a class of one dimensional degenerate/singular parabolic equations, Commun. Pure Appl. Anal. 12 (2013), 1415-1430.
  • [13] G. Fragnelli, Null controllability of degenerate parabolic equations in non divergence form via Carleman estimates, Discrete Contin. Dyn. Syst. Ser. S 6 (2013), 687-701.
  • [14] G. Fragnelli, Interior degenerate/singular parabolic equations in nondive.rge.nce form: well-posedness and Carleman estimates, J. Differential Equations 260 (2016), 1314-1371.
  • [15] G. Fragnelli, D. Mugnai, Carleman estimates and observability inequalities for parabolic equations with interior degeneracy, Advances in Nonlinear Analysis 2 (2013), 339-378.
  • [16] G. Fragnelli, D. Mugnai, Carleman estimates, observability inequalities and null controllability for interior degenerate non smooth parabolic equations, Mem. Amer. Math. Soc. 242 (2016) 1146.
  • [17] G. Fragnelli, D. Mugnai, Corrigendum and improvements to "Carleman estimates, observability inequalities and null controllability for interior degenerate non smooth parabolic equations, and its consequences", to appear in Mem. Amer. Math. Soc.
  • [18] G. Fragnelli, D. Mugnai, Carleman estimates for singular parabolic equations with interior degeneracy and non smooth coefficients, Adv. Nonlinear Anal. 6 (2017), 61-84.
  • [19] G. Fragnelli, D. Mugnai, Singular parabolic equations with interior degeneracy and non smooth coefficients: the Neumann case, to appear in Discrete Contin. Dyn. Syst. Ser. S.
  • [20] G. Fragnelli, D. Mugnai, Controllability of strongly degenerate parabolic problems with strongly singular potentials, Electron. J. Qual. Theory Differ. Equ. 2018, no. 50 , 1-11.
  • [21] G. Fragnelli, G. Ruiz Goldstein, J.A. Goldstein, S. Romanelli, Generators with interior degeneracy on spaces of L2 type, Electron. J. Differential Equations 2012 (2012), 1-30.
  • [22] A. Hajjaj, L. Maniar, J. Salhi, Carleman estimates and null controllability of degenerate/singular parabolic systems, Electron. J. Differential Equations 2016 (2016) 292, pp. 1-25.
  • [23] H. Koch, D. Tataru, Carleman estimates and unique continuation for second order parabolic equations with nonsmooth coefficients, Comm. Partial Differential Equations 34 (2009), 305-366.
  • [24] S. Micu, E. Zuazua, On the lack of null controllability of the heat equation on the half-line, Trans. Amer. Math. Soc. 353 (2001), 1635-1659.
  • [25] B. Muckenhoupt, Hardy's inequality with weights, Collection of articles honoring the completion by Antoni Zygmund of 50 years of scientific activity, I. Studia Math. 44 (1972), 31-38.
  • [26] M. Renardy, R.C. Rogers, An Introduction to Partial Differential Equations, 2nd ed., Texts Appl. Math. 13, Springer, New York, 2004.
  • [27] D.D. Repovs, The Ambrosetti-Prodi problem with degenerate potential and Neumann boundary condition, arXiv: 1802.03194.
  • [28] J. Vancostenoble, Improved Hardy-Poincare inequalities and sharp Carleman estimates for degenerate/singular parabolic problems, Discrete Contin. Dyn. Syst. Ser. S 4 (2011), 761-790.
  • [29] J. Vancostenoble, E. Zuazua, Null controllability for the heat equation with singular inverse-square potentials, J. Funct. Anal. 254 (2008), 1864-1902.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-73dadc84-d99f-44c7-8524-e36b91039b51
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.