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October 2019, 12(5): 1131-1162. doi: 10.3934/krm.2019043
On the blow-up criterion and global existence of a nonlinear PDE system in biological transport networks
Bin Li a,b,
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
Department of Mathematics, Jincheng College of Sichuan University, Chengdu 611731, China
Received January 2019 Revised March 2019 Published July 2019
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.
Keywords: Parabolic-elliptic system, Cauchy problem, blow-up criterion, global solution, biological transport networks.
Mathematics Subject Classification: Primary: 35Q92; Secondary: 35K55; 35J15; 35D35.
Citation: Bin Li. On the blow-up criterion and global existence of a nonlinear PDE system in biological transport networks. Kinetic & Related Models, 2019, 12 (5) : 1131-1162. doi: 10.3934/krm.2019043
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Bin Li