Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-25T01:13:56.180Z Has data issue: false hasContentIssue false
  • English
  • Français

On the solutions of the wave equation with discontinuous derivatives

Published online by Cambridge University Press:  24 October 2008

F. G. Friedlander
F. G. Friedlander
Affiliation:
Trinity CollegeCambridge
Get access Rights & Permissions [Opens in a new window]

Extract

The differential equation of wave propagation is

where u is a variable describing the state of a medium, x, y, z are rectangular coordinates, and r is the time (the time scale is assumed to be such that waves are propagated with unit velocity).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 38 , Issue 4 , November 1942 , pp. 378 - 382
Copyright
Copyright © Cambridge Philosophical Society 1942

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Love, . Wave motions with discontinuities at wave-fronts. Proc. London. Math. Soc. (2) 1 (1903), 37.Google Scholar
Hilbert-Courant, . Methoden der Mathematischen Physik, 2 (Berlin, 1937), 356.CrossRefGoogle Scholar
(2)Hilbert-Courant, . Methoden der Mathematischen Physik, 2 (Berlin, 1937), 364.CrossRefGoogle Scholar
(3)See, for example, Lamp, , Hydrodynamics (6th ed.Cambridge, 1932), p. 494.Google Scholar
(4)Friedlander, . Note on a limit related to the curvatures of two surfaces. Proc. Cambridge Phil. Soc. 38 (1942), 399.CrossRefGoogle Scholar
(5)See, for example, Jeffreys, , Operational Methods in Mathematical Physics (Cambridge, 1931), p. 80.Google Scholar
(6)Frietlander, . The reflexion of sound pulses by convex parabolic reflectors; Proc. Cambridge Phil. Soc. 37 (1941), 149.Google Scholar