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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Global solutions to cross diffusion parabolic systems on 2D domains
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by Dung Le and Vu Thanh Nguyen PDF
Proc. Amer. Math. Soc. 143 (2015), 2999-3010 Request permission

Abstract:

This paper studies global existence of cross diffusion systems on 2-dimensional domains. We assume a quadratic growth on the reaction part and show that a solution exists globally if and only if its total reaction energy does not blow up in finite time. Applications to cross diffusion systems with Lotka-Volterra reaction are presented.
References
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Additional Information
  • Dung Le
  • Affiliation: Department of Mathematics, University of Texas at San Antonio, One UTSA Circle, San Antonio, Texas 78249
  • MR Author ID: 367842
  • Email: dle@math.utsa.edu
  • Vu Thanh Nguyen
  • Affiliation: Department of Mathematics, University of Texas at San Antonio, One UTSA Circle, San Antonio, Texas 78249
  • Received by editor(s): November 12, 2013
  • Received by editor(s) in revised form: March 3, 2014
  • Published electronically: February 13, 2015
  • Additional Notes: The first author was partially supported by NSF grant DMS0707229
  • Communicated by: Catherine Sulem
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 143 (2015), 2999-3010
  • MSC (2010): Primary 35J70, 35B65, 42B37
  • DOI: https://doi.org/10.1090/S0002-9939-2015-12501-4
  • MathSciNet review: 3336624