Wave Equation for Operators with Discrete Spectrum and Irregular Propagation Speed
作者: Michael RuzhanskyNiyaz Tokmagambetov
作者单位: 1Imperial College London
2al–Farabi Kazakh National University
刊名: Archive for Rational Mechanics and Analysis, 2017, Vol.226 (3), pp.1161-1207
来源数据库: Springer Nature Journal
DOI: 10.1007/s00205-017-1152-x
英文摘要: Given a Hilbert space \({\mathcal{H}}\) , we investigate the well-posedness of the Cauchy problem for the wave equation for operators with a discrete non-negative spectrum acting on \({\mathcal{H}}\) . We consider the cases when the time-dependent propagation speed is regular, Hölder, and distributional. We also consider cases when it is strictly positive (strictly hyperbolic case) and when it is non-negative (weakly hyperbolic case). When the propagation speed is a distribution, we introduce the notion of “very weak solutions” to the Cauchy problem. We show that the Cauchy problem for the wave equation with the distributional coefficient has a unique “very weak solution” in an appropriate sense, which coincides with classical or distributional solutions when the latter exist. Examples...
原始语种摘要: Given a Hilbert space \({\mathcal{H}}\) , we investigate the well-posedness of the Cauchy problem for the wave equation for operators with a discrete non-negative spectrum acting on \({\mathcal{H}}\) . We consider the cases when the time-dependent propagation speed is regular, Hölder, and distributional. We also consider cases when it is strictly positive (strictly hyperbolic case) and when it is non-negative (weakly hyperbolic case). When the propagation speed is a distribution, we introduce the notion of “very weak solutions” to the Cauchy problem. We show that the Cauchy problem for the wave equation with the distributional coefficient has a unique “very weak solution” in an appropriate sense, which coincides with classical or distributional solutions when the latter exist. Examples...
全文获取路径: Springer Nature  (合作)
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来源刊物:
影响因子:2.292 (2012)

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关键词翻译
关键词翻译
  • problem 题目
  • consider 仔细考虑
  • operators 操作符
  • anharmonic 非低的
  • strictly 严密地
  • Hamiltonian 哈密(尔)顿
  • compact 紧的
  • propagation 传播
  • notion 概念
  • dependent 从属的