Global solutions and finite time blow up for damped semilinear wave equations

被引：240
作者：
Gazzola, F [1 ]
Squassina, M [1 ]
机构：
[1] Politecn Milan, Dipartimento Matemat, I-20133 Milan, Italy
来源：
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2006年 / 23卷 / 02期
关键词：
damped wave equations; stable and unstable set; global solutions; blowing up solutions; convergence to equilibria; Nehari manifold; mountain pass level;
D O I：
10.1016/j.anihpc.2005.02.007
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A class of damped wave equations with superlinear source term is considered. It is shown that every global solution is uniformly bounded in the natural phase space. Global existence of solutions with initial data in the potential well is obtained. Finally, not only finite time blow up for solutions starting in the unstable set is proved, but also high energy initial data for which the solution blows up are constructed. (c) 2005 Elsevier SAS. All rights reserved.
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页码：185 / 207
页数：23
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