Global nonexistence for a semilinear wave equation with nonlinear boundary dissipation

In this paper, we consider the following problem{ytt−yxx+yt=|y|p−1y,(x,t)∈(0,L)×(0,T),y(0,t)=0,t∈(0,T),yx(L,t)+y(L,t)+|yt(L,t)|m−1yt(L,t)=0,t∈(0,T),y(x,0)=y0(x),yt(x,0)=y1(x),x∈(0,L), where (0,L)(0,L) is a bounded open interval in RR, p>1p>1 and m⩾1m⩾1. We are interested in the interaction between the boundary damping |yt(L,t)|m−1yt(L,t)|yt(L,t)|m−1yt(L,t) and the interior source |y(t)|p−1y(t)|y(t)|p−1y(t). Under some appropriate assumptions on the initial data, two blow-up results with positive initial energy are established. Furthermore, we obtain that the solutions blow up if p   or |y0(L)||y0(L)| is sufficiently large.