On the blow-up criterion and global existence of a nonlinear PDE system in biological transport networks

Bin Li

doi:10.3934/krm.2019043

Article Contents

2019, Volume 12, Issue 5: 1131-1162. Doi: 10.3934/krm.2019043

This issue Previous Article Kinetic methods for inverse problems Next Article Uniform estimates on the Fisher information for solutions to Boltzmann and Landau equations

On the blow-up criterion and global existence of a nonlinear PDE system in biological transport networks

Bin Li^a,b,

a.
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
b.
Department of Mathematics, Jincheng College of Sichuan University, Chengdu 611731, China

Received: January 2019

Revised: March 2019

Published: July 2019

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Abstract

In this paper, we consider a parabolic-elliptic system of partial differential equations in the three dimensional setting that arises in the study of biological transport networks. We establish the local existence of strong solutions and present a blow-up criterion. We also show that the solutions exist globally in time under the some smallness conditions of initial data and of the source.

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Mathematics Subject Classification: Primary: 35Q92; Secondary: 35K55; 35J15; 35D35.

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