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Discrete Dynamics in Nature and Society
Volume 2017, Article ID 2741326, 12 pages
https://doi.org/10.1155/2017/2741326
Research Article

Estimates for Weak Solutions to Nonlinear Degenerate Parabolic Systems

1School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, China
2Department of Mathematics and Statistics, Curtin University, Perth, WA 6845, Australia
3Department of Mathematics, Chongqing Jiaotong University, Chongqing 400074, China

Correspondence should be addressed to Xiangyu Ge; moc.361@eg_uygnaix

Received 24 August 2016; Accepted 13 December 2016; Published 22 January 2017

Academic Editor: Silvia Romanelli

Copyright © 2017 Na Wei et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper is devoted to the estimates for weak solutions to nonlinear degenerate parabolic systems related to Hörmander’s vector fields. The reverse Hölder inequalities for degenerate parabolic system under the controllable growth conditions and natural growth conditions are established, respectively, and an important multiplicative inequality is proved; finally, we obtain the estimates for the weak solutions by combining the results of Gianazza and the Caccioppoli inequality.