Global Existence and Blow-up of Solutions for Parabolic Systems Involving Cross-Diffusions and Nonlinear Boundary Conditions Global Existence and Blow–up of Solutions for Parabolic Systems Involving Cross–Diffusions and Nonlinear Boundary Conditions期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Global Existence and Blow-up of Solutions for Parabolic Systems Involving Cross-Diffusions and Nonlinear Boundary Conditions

作者姓名：

Xiu Hui YANG Fu Cai LI Chun Hong XIE

作者单位：

[1]College of Sciences, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P. R. China [2]Department of Mathematics, Nanjing University, Nanjing 210093, P. R. China

摘要：

Abstract In this paper, we investigate the positive solutions of strongly coupled nonlinear parabolic systems with nonlinear boundary conditions： {ut-a（u, v）△u=g（u, v）, vt-b（u, v）△v=h（u, v）, δu/δη=d（u, v）, δu/δη=f（u, v）.Under appropriate hypotheses on the functions a, b, g, h, d and f, we obtain that the solutions may exist globally or blow up in finite time by utilizing upper and lower solution techniques.

关键词：

非线性抛物线系统交叉扩散非线性边值条件存在性

Global Existence and Blow–up of Solutions for Parabolic Systems Involving Cross–Diffusions and Nonlinear Boundary Conditions

Xiu Hui YANG Fu Cai LI Chun Hong XIE.Global Existence and Blow-up of Solutions for Parabolic Systems Involving Cross-Diffusions and Nonlinear Boundary Conditions[J].Acta Mathematica Sinica,2005,21(4):923-928.

Authors:

Xiu Hui Yang Fu Cai Li Chun Hong Xie

Institution:

(1) College of Sciences, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P. R. China;(2) Department of Mathematics, Nanjing University, Nanjing 210093, P. R. China

Abstract:

In this paper, we investigate the positive solutions of strongly coupled nonlinear parabolic systems with nonlinear boundary conditions:

$\left\{ {\begin{array}{*{20}l} {{u_{t} - a(u,v)\Delta u = g(u,v),} \hfill} & {{v_{t} - b(u,v)\Delta v = h(u,v),} \hfill} \\ {{\frac{{\partial u}} {{\partial \eta }} = d(u,v),} \hfill} & {{\frac{{\partial u}} {{\partial \eta }} = f(u,v).} \hfill} \\ \end{array} } \right.$

Under appropriate hypotheses on the functions a, b, g, h, d and f, we obtain that the solutions may exist globally or blow up in finite time by utilizing upper and lower solution techniques. This work is supported by Youth Science Fund of NUAA

Keywords:

Nonlinear parabolic system Cross-diffusion Nonlinear boundary condition Global existence Blow-up

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