| 具有非局部源与加权非局部边界条件的拟线性抛物方程组 |
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| 引用本文： | 曲程远,姬瑞红,郑斯宁.具有非局部源与加权非局部边界条件的拟线性抛物方程组[J].数学研究及应用,2011,31(5):761-769. |
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| 作者姓名： | 曲程远 姬瑞红 郑斯宁 |
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| 作者单位： | 大连理工大学数学科学学院, 辽宁 大连 116024;成都理工大学数学地质四川省重点实验室， 四川 成都 610059;大连理工大学数学科学学院, 辽宁 大连 116024 |
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| 基金项目： | 国家自然科学基金 (Grant No.11171048). |
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| 摘 要： | In this paper, we investigate the blow-up properties of a quasilinear reaction-diffusion system with nonlocal nonlinear sources and weighted nonlocal Dirichlet boundary conditions. The critical exponent is determined under various situations of the weight functions. It is observed that the boundary weight functions play an important role in determining the blow-up conditions. In addition, the blow-up rate estimate of non-global solutions for a class of weight functions is also obtained, which is found to be independent of nonlinear diffusion parameters m and n.
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| 关 键 词： | quasilinear parabolic system nonlocal boundary conditions critical exponent blow-up rate weight functions. |
| 收稿时间： | 7/8/2010 12:00:00 AM |
| 修稿时间： | 2011/8/28 0:00:00 |
A Quasilinear Parabolic System with Nonlocal Sources and Weighted Nonlocal Boundary Conditions |
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| Cheng Yuan QU,Rui Hong JI and Si Ning ZHENG.A Quasilinear Parabolic System with Nonlocal Sources and Weighted Nonlocal Boundary Conditions[J].Journal of Mathematical Research with Applications,2011,31(5):761-769. |
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| Authors: | Cheng Yuan QU Rui Hong JI and Si Ning ZHENG |
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| Institution: | 1. School of Mathematical Science, Dalian University of Technology, Liaoning 116024, P. R. China
2. Geomathematics Key Laboratory of Sichuan Province, Chengdu University of Technology,Sichuan 610059, P. R. China |
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| Abstract: | In this paper, we investigate the blow-up properties of a quasilinear reaction-diffusion system with nonlocal nonlinear sources and weighted nonlocal Dirichlet boundary conditions. The critical exponent is determined under various situations of the weight functions. It is observed that the boundary weight functions play an important role in determining the blow-up conditions. In addition, the blow-up rate estimate of non-global solutions for a class of weight functions is also obtained, which is found to be independent of nonlinear diffusion parameters $m$ and $n$. |
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| Keywords: | quasilinear parabolic system nonlocal boundary conditions critical exponent blow-up rate weight functions |
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