Finite time blow-up results for the damped wave equations with arbitrary initial energy in an inhomogeneous medium

In this paper we consider the long time behavior of solutions of the initial value problem for the damped wave equation of the form utt − ρ(x) ∆u + ut + m u = f(u) with some ρ(x) and f(u) on the whole space R (n ≥ 3). For the low initial energy case, which is the non-positive initial energy, based on concavity argument we prove the blow up result. As for… CONTINUE READING