ON THE BLOW-UP CRITERION AND GLOBAL EXISTENCE OF A NONLINEAR PDE SYSTEM IN BIOLOGICAL TRANSPORT NETWORKS

Li Bin

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ON THE BLOW-UP CRITERION AND GLOBAL EXISTENCE OF A NONLINEAR PDE SYSTEM IN BIOLOGICAL TRANSPORT NETWORKS

机译：论生物传输网络中非线性PDE系统的爆破准则与全局存在

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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.

机译：在本文中，我们考虑了在生物传输网络研究中出现的三维设置中的部分微分方程的抛物线 - 椭圆形系统。我们建立了强大的解决方案的本地存在，并提出了爆炸标准。我们还表明，在初始数据和源的一些小条件下，全局存在于全局。

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来源
《Kinetic & related models》 |2019年第5期|共32页
作者
Li Bin;
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作者单位

Univ Elect Sci &

Technol China Sch Math Sci Chengdu 611731 Sichuan Peoples R China;

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原文格式 PDF
正文语种 eng
中图分类应用数学;
关键词
Parabolic-elliptic system; Cauchy problem; blow-up criterion; global solution; biological transport networks;

机译：抛物线 - 椭圆体系;Cauchy问题;爆炸标准;全球解决方案;生物传输网络;

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专利

1. ON THE BLOW-UP CRITERION AND GLOBAL EXISTENCE OF A NONLINEAR PDE SYSTEM IN BIOLOGICAL TRANSPORT NETWORKS [J] . Li Bin Kinetic & related models . 2019,第5期

机译：论生物传输网络中非线性PDE系统的爆破准则与全局存在
2. Time global existence and finite time blow-up criterion for solutions to the Keller-Segel system coupled with the Navier-Stokes fluid [J] . Kozono Hideo, Miura Masanari, Sugiyama Yoshie Journal of Differential Equations . 2019,第9期

机译：凯勒 - SEGEL系统与Navier-Stokes流体耦合的解决方案的全局存在和有限时间爆炸标准
3. Local and global existence and blow-up of solutions to a polytropic filtration system with nonlinear memory and nonlinear boundary conditions [J] . Jian Wang, Meng-long Su, Zhong-Bo Fang Bulletin of the Korean Mathematical Society . 2013,第1期

机译：具有非线性记忆和非线性边界条件的多向性过滤系统解的局部和全局存在及爆破
4. Global existence and blow-up solutions for a class of nonlinear reaction diffusion equations under nonlinear boundary flux [C] . Yang Yan, Zhang Lingling Chinese Control and Decision Conference . 2019

机译：非线性边界通量下一类非线性反应扩散方程的整体存在和爆破解
5. Global existence results for near triangular nonlinear parabolic systems. [D] . Luu, Duc Minh. 2010

机译：近似三角形非线性抛物系统的整体存在结果。
6. Global existence and blow-up results for p-Laplacian parabolic problems under nonlinear boundary conditions [O] . Juntang Ding -1

机译：非线性边界条件下p-Laplacian抛物型问题的整体存在和爆破结果
7. LOCAL AND GLOBAL EXISTENCE AND BLOW-UP OF SOLUTIONS TO A POLYTROPIC FILTRATION SYSTEM WITH NONLINEAR MEMORY AND NONLINEAR BOUNDARY CONDITIONS [O] . Jian Wang, Meng-Long Su, Zhong-Bo Fang 2013

机译：具有非线性内存和非线性边界条件的多细胞过滤系统的本地和全球存在和爆破
8. Global Existence for a Semilinear Elliptic-Parabolic PDE System [R] . Li, S. 1991

机译：半线性椭圆 - 抛物型偏微分方程系统的全局存在性

ON THE BLOW-UP CRITERION AND GLOBAL EXISTENCE OF A NONLINEAR PDE SYSTEM IN BIOLOGICAL TRANSPORT NETWORKS

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