The global in time solvability of the one-dimensional nonlinear equations of thermoelasticity, equations of viscoelasticity and nonlinear wave equations in several space dimensions with some boundary dissipation is discussed. The blow up of the solutions which might be possible even for small data is excluded by allowing for a certain dissipative mechanism.
@article{118582,
author = {Yoshihiro Shibata},
title = {Global in time solvability of the initial boundary value problem for some nonlinear dissipative evolution equations},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {34},
year = {1993},
pages = {295-312},
zbl = {0805.35077},
mrnumber = {1241738},
language = {en},
url = {http://dml.mathdoc.fr/item/118582}
}
Shibata, Yoshihiro. Global in time solvability of the initial boundary value problem for some nonlinear dissipative evolution equations. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) pp. 295-312. http://gdmltest.u-ga.fr/item/118582/
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