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Published online by Cambridge University Press: 20 January 2009
The Partial Differential Equations of Physics may be defined as those equations which can be derived from a “least action principle,” that is, as those which are obtained by making a certain integral stationary by the methods of the Calculus of Variations. But, generally speaking, such equations belong to conservative physical systems, and not to those which involve dissipation of energy. In this note it is shewn that a certain class of dissipative equation, of which the best known example is the equation of telegraphy, can be derived from such a calculus of variations problem.
page 61 note * See Emmy Noetker. Gott. Naoh. (1918), p. 238.
page 62 note * See Lie: Leipz ger Berichte (18947–95), p. 322.
page 65 note * Proc. Land. Math. Soc. (1) 4 (1873).
page 66 note * See Rayleigh's Sound I., p. 467.
page 68 note * See Lamb's Hydrodynamics (4th Edn.), p. 609.
page 68 note † See Lamb, loc. cit., p. 575,
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