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A Priori Estimates for a Nonlinear System with Some Essential Symmetrical Structures

1,2,* and 1
1
Department of Mathematics, Jincheng College of Sichuan University, Chengdu 611731, China
2
College of Mathematics, Sichuan University, Chengdu 610064, China
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(7), 852; https://doi.org/10.3390/sym11070852
Received: 18 May 2019 / Revised: 17 June 2019 / Accepted: 20 June 2019 / Published: 2 July 2019
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PDF [265 KB, uploaded 2 July 2019]

Abstract

In this paper, we are concerned with a nonlinear system containing some essential symmetrical structures (e.g., cross-diffusion) in the two-dimensional setting, which is proposed to model the biological transport networks. We first provide an a priori blow-up criterion of strong solution of the corresponding Cauchy problem. Based on this, we also establish a priori upper bounds to strong solution for all positive times. View Full-Text
Keywords: Cauchy problem; a priori estimates; blow-up criterion; global solution; biological transport networks Cauchy problem; a priori estimates; blow-up criterion; global solution; biological transport networks
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 (CC BY 4.0).
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Shen, J.; Li, B. A Priori Estimates for a Nonlinear System with Some Essential Symmetrical Structures. Symmetry 2019, 11, 852.

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