Global well-posedness and global attractor of fourth order semilinear parabolic equation
Corresponding Author
Runzhang Xu
College of Science, Harbin Engineering University, 150001, China
College of Automation, Harbin Engineering University, 150001, China
Differential Equations Research Center, Harbin Engineering University, 150001, China
Correspondence to: Runzhang Xu, College of Science, Harbin Engineering University,150001, China.
E-mail: [email protected]
Search for more papers by this authorTianlong Chen
College of Automation, Harbin Engineering University, 150001, China
Search for more papers by this authorChunmei Liu
College of Automation, Harbin Engineering University, 150001, China
Search for more papers by this authorYunhua Ding
College of Science, Harbin Engineering University, 150001, China
Search for more papers by this authorCorresponding Author
Runzhang Xu
College of Science, Harbin Engineering University, 150001, China
College of Automation, Harbin Engineering University, 150001, China
Differential Equations Research Center, Harbin Engineering University, 150001, China
Correspondence to: Runzhang Xu, College of Science, Harbin Engineering University,150001, China.
E-mail: [email protected]
Search for more papers by this authorTianlong Chen
College of Automation, Harbin Engineering University, 150001, China
Search for more papers by this authorChunmei Liu
College of Automation, Harbin Engineering University, 150001, China
Search for more papers by this authorYunhua Ding
College of Science, Harbin Engineering University, 150001, China
Search for more papers by this authorAbstract
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 Hk(Ω), which attracts any bounded subsets of Hk(Ω) in the Hk-norm. Copyright © 2014 John Wiley & Sons, Ltd.
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