Long Time Behavior of Nonlinear Degenerate Parabolic Equations in Monotone Domains
The nonlinear degenerate parabolic equation in monotone domain has essential difficulties because of its inherent non-au-tonomy and degeneracy.This paper mainly studied the well-posedness of the variational solution of satisfying the energy equality and the existence of the pull-back attractor.First,the penalty method was used to obtain the well-posedness of variational solution of the perturbation equation which satisfies the energy equality.Second,for the perturbed equation,the existence of the limit solution of the equation was attained by the regularity method,further gained the well-posedness of the variational solution of original equa-tion which satisfies the energy equality.Final,based on the well-posedness of variational solutions,we constructed a two-parameter semigroup of non-autonomous dynamical system,and the existence of asymptotically compact pullback absorbing sets for such sys-tem was proved by combining the uniform energy dissipation estimates and the contraction function method,thus,the pull-back at-tractor of this kind of system was established from the preceding analysis.
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