This paper deals with a class of nonlinear viscoelastic wave equation with damping and source terms
utt - △u - △ut - △utt + ∫0tg(t - s)△u(s)ds + ut|ut|m-2=u|u|p-2
with acoustic boundary conditions. Under some appropriate assumption on relaxation function g and the initial data, we prove that the solution blows up in finite time if the positive initial energy satisfies a suitable condition.
Jiali YU
,
Yadong SHANG
,
Huafei DI
. GLOBAL NONEXISTENCE FOR A VISCOELASTIC WAVE EQUATION WITH ACOUSTIC BOUNDARY CONDITIONS[J]. Acta mathematica scientia, Series B, 2020
, 40(1)
: 155
-169
.
DOI: 10.1007/s10473-020-0111-2
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