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