Non-existence of weak solutions to nonlinear damped wave equations in exterior domains

We consider the initial boundary value problem of the nonlinear damped wave equation in an exterior domain ΩΩ, {∂t2u−Δu+∂tu=|u|p,t>0,x∈Ω,u(0,x)=u0(x),∂tu(0,x)=u1(x),x∈Ω,u=0,t>0,x∈∂Ω. When 1