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• W1995335280 abstract "We study the nonlinear viscoelastic wave equation $$ u_{tt} - k_{0} Delta u + int_{0}^{t} g(t-s) mathrm{div} bigr[a(x) nabla u(s) bigr] ds + bigr(k_{1} + b(x) |u_{t}|^{m-2}bigr) u_{t} = |u|^{p-2}u $$ with dissipative boundary conditions. Under some restrictions on the initial data and the relaxation function and without imposing any restrictive assumption on $a(x)$, we show that the rate of decay is similar to that of $g$. We also prove the blow-up results for certain solutions in two cases. In the case $k_{1} = 0$, $m=2$, we show that the solutions blow up in finite time under some restrictions on initial data and for arbitrary initial energy. In another case, $k_{1}geq 0$, $mgeq 2$, we prove a nonexistence result when the initial energy is less than potential well depth." @default.
• W1995335280 created "2016-06-24" @default.
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• W1995335280 date "2013-11-01" @default.
• W1995335280 modified "2023-09-30" @default.
• W1995335280 title "ASYMPTOTIC BEHAVIOR AND BLOW-UP OF SOLUTIONS FOR A NONLINEAR VISCOELASTIC WAVE EQUATION WITH BOUNDARY DISSIPATION" @default.
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• W1995335280 doi "https://doi.org/10.11650/tjm.17.2013.3034" @default.
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