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On the Cauchy Problem Describing an Electron-Phonon Interaction

On the Cauchy Problem Describing an Electron-Phonon Interaction
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摘要 In this paper, a model is derived to describe a quartic anharmonic interatomic interaction with an external potential involving a pair electron-phonon. The authors study the corresponding Cauchy Problem in the semilinear and quasilinear cases.
作者 Joao-Paulo DIAS Mário FIGUEIRA Filipe OLIVEIRA
机构地区 Centro de Matemática e Aplicacoes Fundamentais and Faculdade de Ciencias Centro de Matemática e Aplicacoes
出处 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2011年第4期483-496,共14页 数学年刊（B辑英文版）
基金 Project supported by the Fundacao para a Ciencia e Tecnologia, Financiamento Base (Nos. 2008-ISFL-1-209,2008-ISFL-1-297) the Fundacao para a Ciencia e Tecnologia Grant (No. PTDC/MAT/110613/2009)
关键词 SchrSoinger-like equations Cauchy problem BLOW-UP Phonon-electroninteraction Cauchy问题 相互作用 电子 声子 原子间 拟线性 半线性 四次
分类号 O411 [理学—理论物理]
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参考文献16

  • 1Braun, O. M., Fei, Z., Kivshar, Y. S., et al., Kinks in the Klein-Gordon model with anharmonic interatomic interactions: a variational approach, Physics Letters A, 157, 1991, 241-245.
  • 2Caetano, F., On the existence of weak solutions to the Cauchy problem for a class of quasilinear hyperbolic equations with a source term, Rev. Mat. Complut., 17, 2004, 147-167.
  • 3Dias, J. P. and Figueira, M., Existence of weak solutions for a quasilinear version of Benney equations, J. Hyp. Diff. Eq., 4, 2007, 555-563.
  • 4Dias, J. P., Figueira, M. and Frid, H., Vanishing viscosity with short wave-long wave interactions for systems of conservation laws, Arch. Ration. Mech. Anal., 196, 2010, 981-1010.
  • 5Dias, J. P., Figueira, M. and Oliveira, F., Existence of local strong solutions for a quasilinear Benney system, C. R. Math. Acad. Sci. Paris, 344, 2007, 493-496.
  • 6Ginibre, J., Tsutsumi, Y. and Velo, G., On the Cauchy problem for the Zakharov system, J. Funct. Anal., 151, 1997, 384-486.
  • 7Kato, T., Quasi-linear equations of evolution, with applications to partial differential equations, Lecture Notes in Mathematics, Springer-Verlag, New York, 448, 1975, 25-70.
  • 8Konotop, V., Localized electron-phonon states originated by a three-wave interaction, Physical Review B, 55(18), 1997, Rl1926-R11928.
  • 9Linares, F. and Matheus, C., Well-posedness for the 1D Zakharov-Rubenchik system, Adv. Diff. Eqs., 14, 2009, 261-288.
  • 10Oliveira, F., Stability of the solitons for the one-dimensional Zakharov-Rubenchik equation, Physica D, 175, 2003, 220-240.
Chinese Annals of Mathematics,Series B
2011年 第4期

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