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We discuss the asymptotic behaviour of solutions for the non-local hyperbolic problemwith initial conditions
and
, in the case where
and
is a positive function lying in
. When the initial energy
which corresponds to the problem, is non-negative and small, there exists a unique global solution in time. When the initial energy
is negative, the solution blows-up in finite time. A combination of the modified potential well method and the concavity method is widely used.
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