Blow-up solutions for a string equation with nonlinear boundary source and arbitrary-initial-energy

In this paper, we study the following problem ytt−yxx+yt=0,(x,t)∈(0,L)×(0,T) with the initial–boundary conditions {y(0,t)=0,t∈(0,T),yx(L,t)=|y(L,t)|p−1y(L,t)+by(L,t),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 b≥0b≥0. We get three sufficient conditions for obtaining the blow-up solutions of the problem. Under some restriction on the parameters in the problem, we conclude that, whether the initial energy is positive or negative, the solution blows up whenever bb is large enough.