Blow-up of weak solutions for the semilinear wave equations with nonlinear boundary and interior sources and damping
Tom 35 / 2008
Applicationes Mathematicae 35 (2008), 281-304
MSC: Primary 35L05; Secondary 35B33, 35B35, 35L20.
DOI: 10.4064/am35-3-3
Streszczenie
We focus on the blow-up in finite time of weak solutions to the wave equation with interior and boundary nonlinear sources and dissipations. Our central interest is the relationship of the sources and damping terms to the behavior of solutions. We prove that under specific conditions relating the sources and the dissipations (namely $p > m$ and $k > m$), weak solutions blow up in finite time.
