Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2012-01-01

Journal: CHINESE ANNALS OF MATHEMATICS SERIES B

Included Journals: ISTIC、SCIE

Volume: 33

Issue: 1

Page Number: 107-112

ISSN: 0252-9599

Key Words: Fujita exponent; Liouville type theorem; Higher-order parabolic inequalities; Test function method

Abstract: This paper deals with a coupled system of fourth-order parabolic inequalities |u|(t) >= -Delta(2)u + |v|(q), |v|(t) >= -Delta(2)v + |u|(p) in S = R-n x R+ with p, q > 1, n >= 1. A Fujita-Liouville type theorem is established that the inequality system does not admit nontrivial nonnegative global solutions on S whenever n/4 <= max(p+1/pq-1, q+1/pq-1). Since the general maximum-comparison principle does not hold for the fourth-order problem, the authors use the test function method to get the global non-existence of nontrivial solutions.