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

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 corr...

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Main Authors:	Jieqiong Shen, Bin Li
Format:	Article
Language:	English
Published:	MDPI AG 2019-07-01
Series:	Symmetry
Subjects:	Cauchy problem a priori estimates blow-up criterion global solution biological transport networks
Online Access:	https://www.mdpi.com/2073-8994/11/7/852

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spelling	doaj-c64ce04e95d843df9125ccb7f56e095f2020-11-25T01:42:51ZengMDPI AGSymmetry2073-89942019-07-0111785210.3390/sym11070852sym11070852A Priori Estimates for a Nonlinear System with Some Essential Symmetrical StructuresJieqiong Shen0Bin Li1Department of Mathematics, Jincheng College of Sichuan University, Chengdu 611731, ChinaDepartment of Mathematics, Jincheng College of Sichuan University, Chengdu 611731, ChinaIn 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.https://www.mdpi.com/2073-8994/11/7/852Cauchy problema priori estimatesblow-up criterionglobal solutionbiological transport networks
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Jieqiong Shen Bin Li
spellingShingle	Jieqiong Shen Bin Li A Priori Estimates for a Nonlinear System with Some Essential Symmetrical Structures Symmetry Cauchy problem a priori estimates blow-up criterion global solution biological transport networks
author_facet	Jieqiong Shen Bin Li
author_sort	Jieqiong Shen
title	A Priori Estimates for a Nonlinear System with Some Essential Symmetrical Structures
title_short	A Priori Estimates for a Nonlinear System with Some Essential Symmetrical Structures
title_full	A Priori Estimates for a Nonlinear System with Some Essential Symmetrical Structures
title_fullStr	A Priori Estimates for a Nonlinear System with Some Essential Symmetrical Structures
title_full_unstemmed	A Priori Estimates for a Nonlinear System with Some Essential Symmetrical Structures
title_sort	priori estimates for a nonlinear system with some essential symmetrical structures
publisher	MDPI AG
series	Symmetry
issn	2073-8994
publishDate	2019-07-01
description	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.
topic	Cauchy problem a priori estimates blow-up criterion global solution biological transport networks
url	https://www.mdpi.com/2073-8994/11/7/852
work_keys_str_mv	AT jieqiongshen aprioriestimatesforanonlinearsystemwithsomeessentialsymmetricalstructures AT binli aprioriestimatesforanonlinearsystemwithsomeessentialsymmetricalstructures AT jieqiongshen prioriestimatesforanonlinearsystemwithsomeessentialsymmetricalstructures AT binli prioriestimatesforanonlinearsystemwithsomeessentialsymmetricalstructures
_version_	1725034639325659136

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

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