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Mathematical Notes

, Volume 103, Issue 5–6, pp 856–858 | Cite as

On a Very Weak Solution of the Wave Equation for a Hamiltonian in a Singular Electromagnetic Field

  • M. V. Ruzhansky
  • N. E. Tokmagambetov
Short Communications

Keywords

wave equation Cauchy problem Landau Hamiltonian singular electromagnetic field very weak solution 

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References

  1. 1.
    L. D. Landau and E. M. Lifshits, Theoretical Physics, Vol.3: Quantum Mechanics: Nonrelativistic Theory (Nauka, Moscow, 1986) [in Russian].zbMATHGoogle Scholar
  2. 2.
    A. M. Savchuk and A. A. Shkalikov, Mat. Zametki 66 (6), 897 (1999) [Math. Notes 66 (6), 741 (1999)].CrossRefGoogle Scholar
  3. 3.
    J. Eckhardt, F. Gesztesy, R. Nichols, and G. Teschl, J. Lond. Math. Soc. (2) 88 (3), 801 (2013).MathSciNetCrossRefGoogle Scholar
  4. 4.
    J. Eckhardt, F. Gesztesy, R. Nichols, and G. Teschl, J. Spectr. Theory 4 (4), 715 (2014).MathSciNetCrossRefGoogle Scholar
  5. 5.
    K. A. Mirzoev and T. A. Safonova, Dokl. Ross. Akad. Nauk 441 (2), 165 (2011) [Dokl. Math. 84 (3), 791 (2011)].Google Scholar
  6. 6.
    K. A. Mirzoev and A. A. Shkalikov, Mat. Zametki 99 (5), 788 (2016) [Math. Notes 99 (5), 779 (2016)].MathSciNetCrossRefGoogle Scholar
  7. 7.
    V. E. Vladykina and A. A. Shkalikov, Mat. Zametki 98 (6), 832 (2015) [Math. Notes 98 (6), 891 (2015)].CrossRefGoogle Scholar
  8. 8.
    R. O. Hryniv and Y. V. Mykytyuk, Inverse Problems 19 (3), 665 (2003).MathSciNetCrossRefGoogle Scholar
  9. 9.
    M. I. Neiman-Zade and A. A. Shkalikov, Mat. Zametki 66 (5), 723 (1999) [Math. Notes 66 (5), 599 (1999)].MathSciNetCrossRefGoogle Scholar
  10. 10.
    G. Garetto and M. Ruzhansky, Arch. Ration.Mech. Anal. 217 (1), 113 (2015).MathSciNetCrossRefGoogle Scholar
  11. 11.
    L. Landau, Z. Phys. 64, 629 (1930).CrossRefGoogle Scholar
  12. 12.
    M. Oberguggenberger, Multiplication of Distributions and Applications to Partial Differential Equations (Longman Sci. and Tech., Harlow, 1992).zbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Imperial CollegeLondonGreat Britain
  2. 2.Al-Farabi Kazakh National UniversityAlmatyKazakhstan
  3. 3.Institute of Mathematics and Mathematical ModelingAlmatyKazakhstan

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