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Tytuł artykułu

Remarks on damped Schrodinger equation of Choquard type

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper is devoted to the Schrodinger-Choquard equation with linear damping. Global existence and scattering are proved depending on the size of the damping coefficient.
Rocznik
Strony
465--488
Opis fizyczny
BIbliogr. 30 poz.
Twórcy
  • Qassim University Department of Mathematics College of Science and Arts in Uglat Asugour Kingdom of Saudia Arabia
  • University Tunis El-Manar Department of Mathematics Preparatory Institute for Engineering Studies Elmanar Campus, BP 244 CP 2092, Elmanar 2, Tunis, Tunisia
Bibliografia
  • [1] G.D. Akrivis, V.A. Dougalis, O.A. Karakashian, W.R. Mckinney, Numerical approximation of singular solution of the damped nonlinear Schrödinger equation, [in:] ENUMATH, vol. 97, World Scientific, River Edge, NJ, 1998, 117-124.
  • [2] I.V. Barashenkov, N.V. Alexeeva, E.V. Zemlianaya, Two- and three-dimensional oscil lons in nonlinear Faraday resonance, Phys. Rev. Lett. 89 (2002), 104101.
  • [3] P. Begout, J.I. Diaz, Finite time extinction for the strongly damped nonlinear Schrödinger equation in bounded domains, J. Differ. Equ. 268 (2020), no. 7, 4029-4058.
  • [4] C. Bonanno, P. d’Avenia, M. Ghimenti, M. Squassina, Soliton dynamics for the generalized Choquard equation J. Math. Anal. Appl. 417 (2014), 180-199.
  • [5] R. Carles, P. Antonelli, C. Sparber, On nonlinear Schrödinger type equations with nonlinear damping, Int. Math. Res. Not. 3 (2013), 740-762.
  • [6] T. Cazenave, Semilinear Schrödinger Equations, Lecture Notes in Mathematics, Courant Institute of Mathematical Sciences, New York, 2003.
  • [7] J. Chen, B. Guo, Strong instability of standing waves for a nonlocal Schrödinger equation, Physica D 227 (2007), 142-148.
  • [8] M. Darwich, On the Cauchy problem for the nonlinear Schrödinger equation including fractional dissipation with variable coefficient, Math. Methods Appl. Sci. 41 (2018), 2930-2938.
  • [9] M. Darwich, L. Molinet, Some remarks on the nonlinear Schrödinger equation with fractional dissipation, J. of Math. Phys. 57 (2015), 101502.
  • [10] B. Feng, X. Yuan, On the Cauchy problem for the Schrödinger-Hartree equation, Evol. Equ. Control Theory 4 (2015), no. 4, 431-445.
  • [11] G. Fibich, Self-focusing in the damped nonlinear Schrödinger equation, SIAM J. Appl. Math. 61 (2001), no. 5, 1680-1705.
  • [12] H. Genev, G. Venkov, Soliton and blow-up solutions to the time-dependent Schrödinger-Hartree equation, Discrete Contin. Dyn. Syst. Ser. S 5 (2012), 903-923.
  • [13] M.V. Goldman, K. Rypdal, B. Hafizi, Dimensionality and dissipation in Langmuir col lapse, Phys. Fluids 23 (1980), 945-955.
  • [14] E.P. Gross, E. Meeron, Physics of Many-particle Systems, vol. 1, Gordon Breach, New York, 1966, 231-406.
  • [15] M. Lewin, N. Rougerie, Derivation of Pekar’s polarons from a microscopic model of quantum crystal, SIAM J. Math. Anal. 45 (2013), 1267-1301.
  • [16] E. Lieb, Analysis, 2nd ed., Graduate Studies in Mathematics, Amer. Math. Soc., Providence RI 14, 2001.
  • [17] P.L. Lions, The Choquard equation and related questions, Nonlinear Anal. 4 (1980), 1063-1073.
  • [18] P.L. Lions, Symetrie et compacité dans les espaces de Sobolev, J. Funct. Anal. 49 (1982), 315-334.
  • [19] V. Moroz, J.V. Schaftingen, Ground states of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics, J. Funct. Anal. 265 (2013), 153-184.
  • [20] V. Moroz, J.V. Schaftingen, A guide to the Choquard equation, J. Fixed Point Theory Appl. 19 (2017), 773-813.
  • [21] M. Ohta, G. Todorova, Remarks on global existence and blowup for damped non-linear Schrödinger equations, Discret. Contin. Dyn. Syst. 23 (2009), 1313-1325.
  • [22] L.E. Payne, D.H. Sattinger, Saddle points and instability of non-linear hyperbolic equations, Israel J. Math. 22 (1976), 273-303.
  • [23] R. Penrose, Quantum computation, entanglement and state reduction, Phil. Trans. Roy. Soc. (Lond.) A 356 (1998), 1927-1939.
  • [24] T. Saanouni, Remarks on damped fractional Schrödinger equation with pure power nonlinearity, J. Math. Phys. 56 (2015), 061502.
  • [25] T. Saanouni, Damped non-linear coupled Schrödinger equation, Complex Anal. Oper. Theory 13 (2019), 1093-1110.
  • [26] T. Saanouni, Scattering threshold for the focusing Choquard equation, Nonlinear Differ. Equ. Appl. 26 (2019), Article no. 41.
  • [27] T. Saanouni, Sharp threshold of global wel l-posedness vs finite time blow-up for a class of inhomogeneous Choquard equations, J. Math. Phys. 60 (2019), 081514.
  • [28] T. Tao, Nonlinear Dispersive Equations: Local and Global Analysis, vol. 106, CBMS Regional Conference Series in Mathematics, 2006.
  • [29] M. Tsutsumi, Nonexistence of global solutions to the Cauchy problem for the damped nonlinear Schrödinger equations, SIAM J. Math. Anal. 15 (1984), 357-366.
  • [30] M. Tsutsumi, On global solutions to the initial-boundary value problem for the damped nonlinear Schrödinger equations, J. Math. Anal. Appl. 145 (1990), 328-341.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
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Bibliografia
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