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Global and blow up solutions to cross diffusion systems on 3D domains


Authors: Dung Le and Vu Thanh Nguyen
Journal: Proc. Amer. Math. Soc. 144 (2016), 4845-4859
MSC (2010): Primary 35J70, 35B65; Secondary 42B37
Published electronically: April 20, 2016
MathSciNet review: 3544534
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Abstract: Necessary and sufficient conditions for global existence of classical solutions to a class of cross diffusion systems on 3-dimensional domains are studied. Examples of blow up solutions are also given.


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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
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
Email: vu.nguyen@utsa.edu

DOI: https://doi.org/10.1090/proc/13102
Keywords: Elliptic systems, H\"older regularity, $A_p$ weights, BMO weak solutions
Received by editor(s): November 2, 2014
Received by editor(s) in revised form: January 16, 2016
Published electronically: April 20, 2016
Additional Notes: The second author was partially supported by NSF grant DMS0707229
Communicated by: Catherine Sulem
Article copyright: © Copyright 2016 American Mathematical Society