Elementary solutions of the transport equation and their applications
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Publication:771159
DOI10.1016/0003-4916(60)90060-9zbMath0087.42301OpenAlexW2037693743MaRDI QIDQ771159
Publication date: 1960
Published in: Annals of Physics (Search for Journal in Brave)
Full work available at URL: http://hdl.handle.net/2027.42/32430
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Cites Work