期刊
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
卷 338, 期 2, 页码 1169-1187出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2007.05.076
关键词
generalized double dispersion equations; Cauchy problem; potential wells; global existence; nonexistence
In this paper we study Cauchy problem of generalized double dispersion equations u(tt)-u(xx)-u(xxtt)+u(xxxx)=f(u)(xx), where f (u) = |u|(p), p > 1 or u(2k), k = 1, 2,.... By introducing a family of potential wells we not only get a threshold result of global existence and nonexistence of solutions, but also obtain the invariance of some sets and vacuum isolating of solutions. In addition, the global existence and finite time blow up of solutions for problem with critical initial conditions E (0) = d, I (u(0)) >= 0 or I (u(0)) < 0 are proved. (C) 2007 Elsevier Inc. All rights reserved.
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