Regularity of global attractor for the fourth-order reaction–diffusion equation

In this paper, it is proved that the fourth-order reaction–diffusion equation possesses a global attractor in Sobolev space HkHk for all k>0k>0, which attracts any bounded subset of Hk(Ω)Hk(Ω) in the HkHk-norm by using an iteration procedure, regularity estimates for the linear semigroups and a classical existence theorem of global attractor.

► The equation is rewritten as an abstract equation by introducing appropriate functional spaces.
► An original proof of existence of global solution and of a global attractor for the equation is presented.
► The expression of global solution to a fourth-order reaction–diffusion equation is given.
► Regularity of a global attractor for the equation is obtained by using iteration procedure.