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Global well‐posedness and global attractor of fourth order semilinear parabolic equation
Author(s) -
Xu Runzhang,
Chen Tianlong,
Liu Chunmei,
Ding Yunhua
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3165
Subject(s) - mathematics , attractor , parabolic partial differential equation , order (exchange) , mathematical analysis , partial differential equation , finance , economics
We study the initial boundary value problem of a class of fourth order semilinear parabolic equations. Global existence and nonexistence of solutions with initial data in the potential well are derived. Moreover, by using the iteration technique for regularity estimates, we obtain that for any k ≥ 0, the semilinear parabolic possesses a global attractor in H k (Ω), which attracts any bounded subsets of H k (Ω) in the H k ‐norm. Copyright © 2014 John Wiley & Sons, Ltd.