| A Liouville-Type Theorem for Higher-Order Parabolic Inequalities and Its Applications |
| Received:February 28, 2010 Revised:April 22, 2011 |
| Key Words:
Liouville theorem parabolic inequalities Fujita phenomena.
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| Fund Project:Supported by the Scientific Research Fund of Sichuan Provincial Education Department (Grant No.09ZB081), the Key Scientific Research Foundation of Xihua University (Grant No.Z0912611), Sichuan Youth Science & Technology Foundation (Grant No.2011JQ0003) an |
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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. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2011.05.020 |
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