A Liouville-Type Theorem for Higher-Order Parabolic Inequalities and Its Applications
Received:February 28, 2010  Revised:April 22, 2011
Key Word: Liouville theorem   parabolic inequalities   Fujita phenomena.  
Fund ProjectL: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
Author NameAffiliation
Yu Lan WANG School of Mathematics and Computer Engineering, Xihua University, Sichuan 610039, P. R. China 
Ying WANG School of Mathematical Science, University of Electronic Science and Technology of China, Sichuan 610054, P. R. China 
Zhao Yin XIANG 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.
Citation:
DOI:10.3770/j.issn:1000-341X.2011.05.020
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