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Global existence for a class of triangular parabolic systems on domains of arbitrary dimension


Authors: Dung Le and Toan Trong Nguyen
Journal: Proc. Amer. Math. Soc. 133 (2005), 1985-1992
MSC (2000): Primary 35K57; Secondary 35B65
DOI: https://doi.org/10.1090/S0002-9939-05-07867-6
Published electronically: February 24, 2005
MathSciNet review: 2137864
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Abstract: A class of triangular parabolic systems given on bounded domains of $\mathbb{R}^n$ with arbitrary $n$ is investigated. Sufficient conditions on the structure of the systems are found to assure that weak solutions exist globally.


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Additional Information

Dung Le
Affiliation: Department of Applied Mathematics, University of Texas at San Antonio, 6900 North Loop 1604 West, San Antonio, Texas 78249
Email: dle@math.utsa.edu

Toan Trong Nguyen
Affiliation: Department of Applied Mathematics, University of Texas at San Antonio, 6900 North Loop 1604 West, San Antonio, Texas 78249
Email: toan.nguyen@utsa.edu

DOI: https://doi.org/10.1090/S0002-9939-05-07867-6
Keywords: Cross diffusion systems, boundedness, H\"older regularity
Received by editor(s): February 15, 2004
Published electronically: February 24, 2005
Additional Notes: The first author was supported in part by NSF Grant #DMS0305219, Applied Mathematics Program.
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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