Publication Cover
Applicable Analysis
An International Journal
Volume 103, 2024 - Issue 4
107
Views
1
CrossRef citations to date
0
Altmetric
Research Article

Scattering for a class of inhomogeneous generalized Hartree equations

ORCID Icon &
Pages 790-806 | Received 19 Jul 2022, Accepted 20 Feb 2023, Published online: 03 May 2023

References

  • Alharbi MG, Saanouni T. Sharp threshold of global well-posedness vs finite time blow-up for a class of inhomogeneous Choquard equations. J Math Phys. 2019;60:081514.
  • Alkhidhr HA. Closed-form solutions to the perturbed NLSE with Kerr law nonlinearity in optical fibers. Results Phys. 2021;22:Article ID: 103875.
  • Fröhlich J, Lenzmann E. Mean-field limit of quantum Bose gases and nonlinear Hartree equation, Séminaire: Equations aux Dérivées Partielles 2003–2004, Sémin. Équ. Dériv. Partielles, Ecole Polytech., Palaiseau, Exp. no. XIX, 2004. p. 26.
  • Gross EP. Physics of many-particle systems. Vol. 1, New York: Gordon Breach; 1996.
  • Moroz IM, Penrose R, Tod P. Spherically-symmetric solutions of the Schrödinger–Newton equations. Class Quantum Gravity. 1998;15(9):2733–2742.
  • Abdulwahab A. Stochastic solutions to the non-linear Schrodinger equation in optical fiber. Thermal Science. 2022; 26(1):185-190.
  • Lions P-L. Some remarks on Hartree equation. Nonlinear Anal. 1981;5:1245–1256.
  • Mohamed EMA, Ahmed NIA, Hussein MIB, et al. Explanation of pressure effect for high temperature superconductors using pressure dependent Schrödinger equation and string theory. Nat Sci. 2020;12(1):28–34.
  • Spohn H. On the Vlasov hierarchy. Math Method Appl Sci. 1981;3:445–455.
  • Alghamdi AM, Gala S, Ragusa MA. Global regularity for the 3D micropolar fluid flows. Filomat. 2022;36(6):1967–1970.
  • Boulaaras S, Chouch A, Ouchenane D. General decay and well-posedness of the Cauchy problem for the Jordan–Moore–Gibson–Thompson equation with memory. Filomat. 2021;35(5):1745–1773.
  • Zhang L, Yang R, Zhang L, et al. A conservative Crank–Nicolson Fourier spectral method for the space fractional Schrödinger equation with wave operators. J Funct Spaces. 2021;2021:Article ID 5137845.
  • Ghanmi R, Saanouni T. Inhomogeneous coupled non-linear Schrödinger systems. J Math Phys. 2021;62:101508.
  • Caoa D, Su Y. Minimal blow-up solutions of mass-critical inhomogeneous Hartree equation. J Math Phys. 2013;54: Article ID: 121511.
  • Saanouni T. Sharp threshold of global well-posedness vs finite time blow-up for a class of inhomogeneous Choquard equations. J Math Phys. 2019;60:081514.
  • Saanouni T, Xu C. Scattering theory for a class of radial focusing inhomogeneous Hartree equations. Potential Anal. 2023;58:617–643.
  • Xu C. Scattering for the non-radial focusing inhomogeneous nonlinear Schrödinger–Choquard equation, Available at http://arxiv.org/abs/2104.09756v1.
  • Aksoy NY, Sarıahmet E. On the stability of finite difference scheme for the Schrödinger equation including momentum operator. Turk J Sci. 2022;7(2):107–115.
  • Iskenderov AD, Yagubov GY. Optimal control problem with unbounded potential for multidimensional, nonlinear and nonstationary Schrödinger equation, Proceedings of the Lankaran State University, Natural Sciences Series; 2007. p. 3–56.
  • Ogunniran M, Alabi A, Amobi Q, et al. Fourth derivative block method for solving two-point singular boundary value problems and related stiff problems. Turk J Sci. 2021;6(2):50–60.
  • Ragusa MA, Tachikawa A. Regularity for minimizers for functionals of double phase with variable exponents. Adv Nonlinear Anal. 2020;9:710–728.
  • Şener SS, Celık E, Özdemir E. The solution of linear Volterra integral equation of the first kind with ZZ-Transform. Turk J Sci. 2021;6(3):127–133.
  • Toyoglu F, Yagubov G. Numerical solution of an optimal control problem governed by two dimensional Schrödinger equation. Appl Comput Math. 2015;4(2):30–38.
  • Kenig CE, Merle F. Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrödinger equation in the radial case. Invent Math. 2006;166(3):645–675.
  • Tao T. On the asymptotic behavior of large radial data for a focusing non-linear Schrödinger equation. Dyn Partial Differ Equ. 2004;1(1):1–47.
  • Dodson B, Murphy J. A new proof of scattering below the ground state for the 3D radial focusing cubic NLS. Proc Amer Math Soc. 2017;145(11):4859–4867.
  • Dinh VD. A unified approach for energy scattering for focusing nonlinear Schrödinger equations. Discr Cont Dyn Syst. 2020;40(11):6441–6471.
  • Moroz V, Schaftingen JV. Groundstates of non-linear Choquard equations: existence, qualitative properties and decay asymptotics. J Funct Anal. 2013;265:153–184.
  • Wang T, Yi T. Uniqueness of positive solutions of the Choquard type equations. Appl Anal. 2017;96(3):409–417.
  • Xiang CL. Uniqueness and nondegeneracy of ground states for Choquard equations in three dimensions. Calc Var. 2016;55(6).
  • Saanouni T. Scattering versus blow-up beyond the threshold for the focusing Choquard equation. J Math Anal Appl. 2020;492(1): Article ID: 124436.
  • Foschi D. Inhomogeneous Strichartz estimates. J Hyperbolic Differ Equ. 2005;2(1):1–24.
  • Keel M, Tao T. Endpoint Strichartz estimates. Amer J Math. 1998;120(5):955–980.
  • Lieb E. Analysis. 2nd ed., Providence, RI: Amer. Math. Soc.; 2001. (Graduate Studies in Mathematics; Vol. 14).

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.