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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am35-3-3,
author = {Lorena Bociu and Irena Lasiecka},
title = {Blow-up of weak solutions for the semilinear wave equations with nonlinear boundary and interior sources and damping},
journal = {Applicationes Mathematicae},
volume = {35},
year = {2008},
pages = {281-304},
zbl = {1152.35416},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am35-3-3}
}
Lorena Bociu; Irena Lasiecka. Blow-up of weak solutions for the semilinear wave equations with nonlinear boundary and interior sources and damping. Applicationes Mathematicae, Tome 35 (2008) pp. 281-304. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am35-3-3/