Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

Global solutions to cross diffusion parabolic systems on 2D domains


Authors: Dung Le and Vu Thanh Nguyen
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
Published electronically: February 13, 2015
MathSciNet review: 3336624
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 35J70, 35B65, 42B37

Retrieve articles in all journals with MSC (2010): 35J70, 35B65, 42B37


Additional Information

Dung Le
Affiliation: Department of Mathematics, University of Texas at San Antonio, One UTSA Circle, San Antonio, Texas 78249
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

DOI: https://doi.org/10.1090/S0002-9939-2015-12501-4
Keywords: Parabolic systems, global existence
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
Article copyright: © Copyright 2015 American Mathematical Society

American Mathematical Society