A class of fourth-order parabolic equation with arbitrary initial energy. (October 2018)

• Record Type: Journal Article
• Authors: Han, Yuzhu
• Is Part Of: Nonlinear analysis. Volume 43(2018)
• Page Start: 451
• Page End: 466
• Publication Date: 2018-10
• Subjects: Fourth-order equation -- Potential well method -- Initial energy -- Global existence -- Blow up; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2018.03.009
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper we apply the modified potential well method to the study of the long time behaviors of solutions to a class of fourth-order parabolic equation in a bounded smooth domain of R n for arbitrary n ≥ 1 . Global existence and blow up in finite time of solutions are obtained when the initial data satisfy different conditions. To be a little more precise, we give a threshold result for the solutions to exist globally or to blow up in finite time when the initial energy is subcritical and critical, respectively. Moreover, the decay rate of the L 2 norm is also obtained for global solutions. Sufficient conditions for the existence of global and blow-up solutions are also provided for supercritical initial energy. These improve and generalize some recent results.