Archive for Rational Mechanics and Analysis

, Volume 216, Issue 3, pp 881–903 | Cite as

Green’s Functions of Wave Equations in \(\mathbb{R}^n_+\times \mathbb{R}_+\)

  • Shijin Deng
  • Weike Wang
  • Shih-Hsien YuEmail author


We study the d’Alembert equation with a boundary. We introduce the notions of Rayleigh surface wave operators, delayed/advanced mirror images, wave recombinations, and wave cancellations. This allows us to obtain the complete and simple formula of the Green’s functions for the wave equation with the presence of various boundary conditions. We are able to determine whether a Rayleigh surface wave is active or virtual, and study the lacunas of the wave equation in three dimensional with the presence of a boundary in the case of a virtual Rayleigh surface wave.


Wave Equation Surface Wave Fundamental Solution Rayleigh Wave Neumann Boundary Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of MathematicsShanghai Jiao Tong UniversityShanghaiChina
  2. 2.Department of MathematicsNational University of SingaporeSingaporeSingapore

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