BACKWARDS DYNAMICS OF TIME-DEPENDENT ATTRACTOR FOR PLATE EQUATION ON THE WHOLE SPACE

In this paper, we give the definition and criterion for the existence of backwards compact time-dependent attractor which is the minimal one among the backwards compact and pullback attracting sets in time-dependent whole space. Combining with the method of $ C_t- $limit compact and backwards asymptotic estimates outside a ball, the existence of backwards compact time-dependent attractor for stretchable plate equation with localized weak damping on the whole space is obtained.