본문 바로가기
KERD
논문KCI 등재

Remarks on nonlinear Dirac equations in one space dimension

허형진
대한수학회 (The Korean Mathematical Society)|2015.07|대한수학회논문집 (Communications of the KMS)|제30권 제3호|pp. 201-208

1

조회

0

다운로드

0

인용

0

참고문헌

키워드

global existencenonlinear Dirac equationsfinite time blow up
주제분류수학

초록

This paper reviews recent mathematical progresses made on the study of the initial-value problem for nonlinear Dirac equations in one space dimension. We also prove the global existence of solutions to some nonlinear Dirac equations and propose a model problem \eqref{model21}.

Abstract

This paper reviews recent mathematical progresses made on the study of the initial-value problem for nonlinear Dirac equations in one space dimension. We also prove the global existence of solutions to some nonlinear Dirac equations and propose a model problem \eqref{model21}.

참고문헌 (15)

  1. D. Agueev, "Modeling of wave resonances in low-contrast photonic crystals", SIAM J. Appl. Math, 65(4), pp.1101~1129 (2005)
  2. T. Candy, "Global existence for an L2 critical nonlinear Dirac equation in one dimension", Adv. Differential Equations, 16(7-8), pp.643~666 (2011)
  3. A. Contreras, "L2 orbital stability of Dirac solitons in the massive Thirring model", arXiv:1312.1019, ~
  4. V. Delgado, "Global solutions of the Cauchy problem for the (classical) coupled Maxwell-Dirac and other nonlinear Dirac equations in one space dimension", Proc. Amer. Math. Soc, 69(2), pp.289~296 (1978)
  5. R. H. Goodman, "Nonlinear propagation of light in one-dimensional periodic structures", J. Nonlinear Sci, 11(2), pp.123~168 (2001)
  6. L. Haddad, "The nonlinear Dirac equations in Bose-Einstein condensates: I. Relativistic solitons in armchair and zigzag geometries", arxiv:1305.6532v2, ~
  7. H. Huh, "Global strong solution to the Thirring model in critical space", J. Math. Anal. Appl, 381(2), pp.513~520 (2011)
  8. H. Huh, "Global strong solutions to some nonlinear Dirac equations in super-critical space", Abstr. Appl. Anal, pp.8~ (2013)
  9. H. Huh, "Global solutions to Gross-Neveu equation", Lett. Math. Phys, 103(8), pp.927~931 (2013)
  10. H. Huh, "Low regularity well-posedness for Gross-Neveu equations", Comm. Pure Appl. Anal, 14(5), pp.1903~1913 (2015)
  11. D. Pelinovsky, "Survey on global existence in the nonlinear Dirac equations in one spatial dimension, Harmonic analysis and nonlinear partial differential equations", pp.37~50 (2011), RIMS Kˆokyˆuroku Bessatsu
  12. D. Pelinovsky, "Orbital stability of Dirac solitons", Lett. Math. Phys, 104(1), pp.21~41 (2014)
  13. S. Selberg, "Low regularity well-posedness for some nonlinear Dirac equations in one space dimension", Differential Integral Equations, 23(3-4), pp.265~278 (2010)
  14. J. Stubbe, "Exact localized solutions of a family of two-dimensional nonlinear spinor fields", J. Math. Phys, 27(10), pp.2561~2567 (1986)
  15. Y. Zhang, "Global strong solution to a nonlinear Dirac type equation in one dimension", Nonlinear Anal, 80, pp.150~155 (2013)

관련 논문AI추천

Local well-posedness of Dirac equations with nonlinearity derived from honeycomb structure in 2 dimensions이기연대한수학회 · 대한수학회보2021 · 제58권 제6호Nonrelativistic limit of Chern-Simons gauged field equations임지현, 채명주대한수학회 · 대한수학회논문집2018 · 제33권 제3호Scattering for the Dirac-Klein-Gordon system with pseudoscalar source and resonant interaction양창훈, 조용근대한수학회 · 대한수학회보2024 · 제61권 제5호On the growth rate of solutions to Gross-Neveu and Thirring equations허형진대한수학회 · 대한수학회논문집2014 · 제29권 제2호Mild solutions for the relativistic Vlasov-Klein-Gordon systemMeixia Xiao, Xianwen Zhang대한수학회 · 대한수학회보2019 · 제56권 제6호Global solutions of semirelativistic Hartree type equations조용근, Tohru Ozawa대한수학회 · 대한수학회지2007 · 제44권 제5호

이 간행물의 다른 논문 (16건)

Hesitant fuzzy bi-ideals in semigroups송석준, 이경자, 전영배pp. 143-154Filters of residuated lattices based on soft set theory노은환, 박철환, 전영배, 이경자pp. 155-168Numerical range and SOT-convergencyAbdolaziz Abdollahi, Mohammad Taghi Heydaripp. 169-176Convergence theorems for a pair of asymptotically and multivalued nonexpansive mapping in CAT(0) spacesNaknimit Akkasriworn, Kritsana Sokhumapp. 177-189Certain new generating relations for products of two Laguerre polynomials최준상, Arjun Kumar Rathiepp. 191-200
원문 보기