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| Fujita-Liouville Type Theorem for Coupled Fourth-Order Parabolic Inequalities |
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Citation： |
Zhaoxin JIANG,Sining ZHENG.Fujita-Liouville Type Theorem for Coupled Fourth-Order Parabolic Inequalities[J].Chinese Annals of Mathematics B,2012,33(1):107~112 |
| Page view： 2732
Net amount： 1965 |
Authors： |
Zhaoxin JIANG; Sining ZHENG; |
Foundation： |
the National Natural Science Foundation of China (Nos. 10771024, 11171048) and the Fundamental Research Funds for the Central Universities (No. 851011). |
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| Abstract： |
This paper deals with a coupled system of fourth-order parabolic inequalities|u|t ≥ ?Δ2u + |v|q, |v|t ≥ ?Δ2v + |u|p in S = Rn × R+ with p, q > 1, n ≥ 1. A Fujita-Liouville type theorem is established that the inequality system does not admit nontrivialnonnegative global solutions on S whenever n4≤ max( p+1pq?1 , q+1pq?1 ). Since the generalmaximum-comparison principle does not hold for the fourth-order problem, the authorsuse the test function method to get the global non-existence of nontrivial solutions. |
Keywords： |
Fujita exponent, Liouville type theorem, Higher-order parabolic inequalities, Test function method |
Classification： |
35B33,35K30,35K55 |
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