On the global solvability of the initial-boundary value problem for a composite-type nonlinear equation (Q1395297)

The goal of this paper is to analyze the existence and nonexistence of a global solution to the following initial-boundary value problem for the composite-type nonlinear equation: \[ u_{tt}-{\alpha}u_{xx}-{\beta}u_{xxtt}=f(u_{xx}), \] \[ u(x,0)=u_0(x),\quad u_t(x,0)=u_1(x),\quad u(0,t)=u(1,t)=0. \] This equation describes waves in media with high-frequency dispersion and model nonlinearity. Conditions on the initial data are established that ensure the global solvability and blowup of a classical solution in a finite time.