caa a22 4500 605515050 CHVBK 20210128100707.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s00205-014-0821-2 doi (NATIONALLICENCE)springer-10.1007/s00205-014-0821-2 Green's Functions of Wave Equations in $$\mathbb{R}^n_+\times \mathbb{R}_+$$ R + n × R + [Elektronische Daten] [Shijin Deng, Weike Wang, Shih-Hsien Yu] 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. Springer-Verlag Berlin Heidelberg, 2014 Deng Shijin Department of Mathematics, Shanghai Jiao Tong University, 200240, Shanghai, China aut Wang Weike Department of Mathematics, Shanghai Jiao Tong University, 200240, Shanghai, China aut Yu Shih-Hsien Department of Mathematics, National University of Singapore, 119076, Singapore, Singapore aut Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 216/3(2015-06-01), 881-903 0003-9527 216:3<881 2015 216 205 https://doi.org/10.1007/s00205-014-0821-2 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00205-014-0821-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Deng Shijin Department of Mathematics, Shanghai Jiao Tong University, 200240, Shanghai, China aut NATIONALLICENCE 700 1- Wang Weike Department of Mathematics, Shanghai Jiao Tong University, 200240, Shanghai, China aut NATIONALLICENCE 700 1- Yu Shih-Hsien Department of Mathematics, National University of Singapore, 119076, Singapore, Singapore aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 216/3(2015-06-01), 881-903 0003-9527 216:3<881 2015 216 205