  The paper is devoted to the study of the backward behavior of solutions of
the initial boundary value problem for the chevron pattern equations under
homogeneous Dirichlet's boundary conditions. We prove that, as $t\rightarrow
\infty$, the asymptotic behavior of solutions of the considered problem is
completely determined by the dynamics of a finite set of functionals.
Furthermore, we provide numerical evidence for the blow-up of certain solutions
of the backward problem in finite time in 1D.
