A Liouville-Type Theorem for Higher-Order Parabolic Inequalities and Its Applications

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Yu Lan WANG Ying WANG Zhao Yin XIANG School of Mathematics and Computer Engineering Xihua University Sichuan P R China School of Mathematical Science University of Electronic Science and Technology of China Sichuan P R China [1 ,2 ,2 ,1 ,610039 ,2 ,610054 ]
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数学研究与评论 | 2011年 / 31卷 / 05期
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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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页码：930 / 936
页数：7
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