山西大学学报（自然科学版）2024，Vol.47Issue(4)：677-690,14.DOI:10.13451/j.sxu.ns.2023093
单调区域上非线性退化抛物方程的长时间性态
Long Time Behavior of Nonlinear Degenerate Parabolic Equations in Monotone Domains
摘要
Abstract
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.关键词
退化抛物方程/单调区域/惩罚法/适定性/拉回吸引子Key words
degenerate parabolic equation/monotone domains/penalty method/well-posedness/pull-back attractor分类
数理科学引用本文复制引用
李心,褚锦芳..单调区域上非线性退化抛物方程的长时间性态[J].山西大学学报（自然科学版）,2024,47(4):677-690,14.基金项目
国家自然科学基金(11801493) （11801493）
河北省自然科学基金(A2022203004) （A2022203004）
河北省教育厅高等学校科技计划青年基金项目(QN2020203) （QN2020203）
