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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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On explosions of solutions to a system of partial differential equations modelling chemotaxis
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by W. Jäger and S. Luckhaus PDF
Trans. Amer. Math. Soc. 329 (1992), 819-824 Request permission

Abstract:

A system of partial differential equations modelling chemotactic aggregation is analysed (Keller-Segel model). Conditions on the system of parameters are given implying global existence of smooth solutions. In two space dimensions and radially symmetric situations, explosion of the bacteria concentration in finite time is shown for a class of initial values.
References
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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 329 (1992), 819-824
  • MSC: Primary 35Q80; Secondary 35B05, 92C45
  • DOI: https://doi.org/10.1090/S0002-9947-1992-1046835-6
  • MathSciNet review: 1046835