In this paper, we consider the following nonlinear viscoelastic wave equation with variable exponents:\[u_{tt}-\Delta u+\int_{0}^{t}g(t-\tau)\Delta u(x,\tau){\rm d}\tau +\mu u_t=|u|^{p(x)-2}u,\] where $\mu$ is a nonnegative constant and the exponent of nonlinearity $p(\cdot)$ and $g$ are given functions. Under arbitrary positive initial energy and specific conditions on the relaxation function $g$, we prove a finite-time blow-up result. We also give some numerical applications to illustrate our theoretical results.
Ala A. TALAHMEH
,
Salim A. MESSAOUDI
,
Mohamed ALAHYANE
. THEORETICAL AND NUMERICAL STUDY OF THE BLOW UP IN A NONLINEAR VISCOELASTIC PROBLEM WITH VARIABLE-EXPONENT AND ARBITRARY POSITIVE ENERGY[J]. Acta mathematica scientia, Series B, 2022
, 42(1)
: 141
-154
.
DOI: 10.1007/s10473-022-0107-y
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