Long-time behavior of solutions of some doubly nonlinear equation

Abstract

The subject of this investigation is the qualitative properties of solutions of the equation where nonlinear term g is supposed to satisfy the upper polynomial growth condition of arbitrary order gðsÞs c s j j q þ kðq ! 0Þ and g 0 (s) > Àl. The existence of a ðW 0 1 2p1 þ 2 ðÞ, C 1þ ðÞÞ-global attractor for this equation with Dirichlet boundary condition is proved.