期刊
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
卷 74, 期 6, 页码 2425-2437出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.na.2010.11.045
关键词
Multidimensional generalized Boussinesq equation; Cauchy problem; Global existence; Blow up; Potential well
资金
- National Natural Science Foundation of China [10871055, 10926149]
- Ph.D. Programs Foundation of Ministry of Education of China [20102304120022]
- Natural Science Foundation of Heilongjiang Province [A200702, A200810]
- Science and Technology Foundation of Education Office of Heilongjiang Province [11541276]
- Foundational Science Foundation of Harbin Engineering University
- Fundamental Research Funds for the Central University [HEUCF20101101]
In this paper, we study the Cauchy problem for a class of the multidimensional Boussinesq-type equation u(tt) - Delta u + Delta(2)u + Delta(2)u(tt) = Delta f(u), where f(u) = +/- a vertical bar u vertical bar(p) or -a vertical bar u vertical bar(p-1)u, a > 0 is a constant. First, we establish a local existence theorem for the solution. Then, for m = 1 (n = 1), m = 2, 3, 4 (n <= 3), we prove the existence of a global H-m solution. Finally, we prove the global nonexistence and finite-time blow up of the solution. (C) 2010 Elsevier Ltd. All rights reserved.
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