Calculus of Variations and Geometric Measure Theory
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F. Gazzola - M. Squassina

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

created by gazzola on 19 Jan 2005
modified on 30 May 2005


Accepted Paper

Inserted: 19 jan 2005
Last Updated: 30 may 2005

Year: 2004


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.

Keywords: potential well theory, dissipative hyperbolic equations


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