| 高阶抛物不等式组的Liouville型定理及其应用 |
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| 引用本文： | 王玉兰,王莹,向昭银.高阶抛物不等式组的Liouville型定理及其应用[J].数学研究及应用,2011,31(5):930-936. |
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| 作者姓名： | 王玉兰 王莹 向昭银 |
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| 作者单位： | 西华大学数学与计算机学院，四川 成都 610039;电子科技大学数学科学学院, 四川 成都 610054;电子科技大学数学科学学院, 四川 成都 610054 |
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| 基金项目： | 四川省教育厅青年基金(Grant No.09ZB081),西华大学重点科研基金(Grant No.Z0912611),四川省青年科技基金(Grant No.2011JQ0003),中央高校基本科研业务费. |
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| 摘 要： | In this paper, we establish a Liouville-type theorem for a system of higher-order parabolic inequalities by using the method of test functions and an integral estimate. As an application, we observe the Fujita blow-up phenomena for the corresponding parabolic system, which in particular fills up the gap in the recent result of Pang et. al. （Existence and nonexistence of global solutions for a higher-order semilinear parabolic system, Indiana Univ. Math. J., 55（2006）, 1113-1134）. Moreover, the importance of this observation is that we do not impose any regularity assumption on the initial data.
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| 关 键 词： | Liouville theorem parabolic inequalities Fujita phenomena. |
| 收稿时间： | 2010/2/28 0:00:00 |
| 修稿时间： | 2011/4/22 0:00:00 |
A Liouville-Type Theorem for Higher-Order Parabolic Inequalities and Its Applications |
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| Yu Lan WANG,Ying WANG and Zhao Yin XIANG.A Liouville-Type Theorem for Higher-Order Parabolic Inequalities and Its Applications[J].Journal of Mathematical Research with Applications,2011,31(5):930-936. |
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| Authors: | Yu Lan WANG Ying WANG and Zhao Yin XIANG |
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| Institution: | 1. School of Mathematics and Computer Engineering, Xihua University,Sichuan 610039, P. R. China
2. School of Mathematical Science, University of Electronic Science and Technology of China,Sichuan 610054, P. R. China |
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| Abstract: | In this paper, we establish a Liouville-type theorem for a system of higher-order parabolic inequalities by using the method of test functions and an integral estimate. As an application, we observe the Fujita blow-up phenomena for the corresponding parabolic system, which in particular fills up the gap in the recent result of Pang et. al. (Existence and non-existence of global solutions for a higher-order semilinear parabolic system, Indiana Univ. Math. J., 55(2006), 1113-1134). Moreover, the importance of this observation is that we do not impose any regularity assumption on the initial data. |
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| Keywords: | Liouville theorem parabolic inequalities Fujita phenomena |
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