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Eighty years of Sommerfeld’s radiation condition. (English) Zbl 0763.01020

This is a very thorough and clearly written article explaining the motivation for Sommerfeld’s introduction of his “radiation condition” to guarantee uniqueness of the solution of certain partial differential equations, and its derivation. Although the condition was first introduced in 1912, the motivation can be traced back to Sommerfeld’s Habilitationsschrift of 1896 (written under the supervision of Felix Klein). Later refinement and developments of the condition by Magnus, Rellich and others are also discussed. In Sommerfeld’s own phrase, the subject matter dealt with is “physical mathematics”, that is, the physical motivation of mathematical methods.

MSC:

01A60 History of mathematics in the 20th century
78A40 Waves and radiation in optics and electromagnetic theory
35-03 History of partial differential equations

Biographic References:

Sommerfeld, A.
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