Asymptotic behavior for solutions of parabolic equations with natural growth terms and irregular data

In this paper we deal with the asymptotic behavior of solution for quasilinear parabolic equations with absorbing lower-order terms whose model is $\[\cases{u_{t}-\Delta u+u|\nabla u|^{2}=f& \mbox{in} \varOmega \times(0,T),\cr\noalign{\vspace{3pt}}u(x,0)=u_{0}& \mbox{in} \varOmega ,}\]$ with L¹ data that do not depend on time. The main result states that, under suitable assumptions, the solution of the parabolic problem converges to the stationary solution.