Blow-up of solutions of a non-linear wave equation with fractional
damping and infinite memory
We consider a non-linear wave equation with an internal fractional
damping, a polynomial source and an infinite memory. Using the
semi-group theory, we get the existence of a local weak solution.
Moreover, we show under some conditions, local solutions may blow up a
in finite time; this is achieved by constructing a suitable Lyapunov