Existence of global attractors for a nonlinear wave equation (Q2484581)

The authors deal with a initial-boundary value problem for a wave equation involving the term \(u_{tx}\) as follows \[ u_{tt}- u_{xx}+\alpha u_{tx}+\beta u_t+ f(u)= h(x),\quad 0< x<\ell,\tag{1} \] \[ u(x,0)= u_0(x),\;u_t(x,0)= u_1(x),\quad 0< x< \ell,\tag{2} \] \[ u(0,t)= u(\ell,t)= 0,\quad t\in \mathbb{R}^+.\tag{3} \] The goal of the authors is to study the long-time behaviour of solutions (1)--(3) and to prove the existence of a global attractor.