Non-existence results for stochastic wave equations in one dimension

The purpose of this paper is to extend recent results [2] and [10] for the stochastic heat equation wave given by|?2u(t,x)?t2=?2u(t,x)?x2+?(u(t,x))W?(t,x)+b(u(t,x)),x?D??D,t>0,u(0,x)=u0(x),??tu(0,x)=v0(x),x?D, where W? space-time white noise, ? a real-valued globally Lipschitz function but b assumed be only locally continuous. Three types domain conditions are studied: D=[0,1] with homogeneous Dirichlet boundary conditions, D=[0,2?] periodic D=R. Then, under suitable following integrability condition???1[?2+2??sb(r)dr]1/2ds0 ?>0, studied in relation non-existence global solutions.