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On blowup for gain‐term‐only classical and relativistic Boltzmann equations
Author(s) -
Andréasson Håkan,
Calogero Simone,
Illner Reinhard
Publication year - 2004
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.555
Subject(s) - term (time) , boltzmann equation , mathematics , boltzmann constant , collision , mathematical analysis , mathematical physics , physics , computer science , quantum mechanics , computer security
We show that deletion of the loss part of the collision term in all physically relevant versions of the Boltzmann equation, including the relativistic case, will in general lead to blowup in finite time of a solution and hence prevent global existence. Our result corrects an error in the proof given ( Math. Meth. Appl. Sci . 1987; 9 :251–259), where the result was announced for the classical hard sphere case; here we give a simpler proof which applies much more generally. Copyright © 2004 John Wiley & Sons, Ltd.