Global well-posedness, asymptotic behavior and blow-up of solutions for a class of degenerate parabolic equations. (July 2020)

• Record Type: Journal Article
• Authors: Liu, Yang; Yu, Tao; Li, Wenke
• Is Part Of: Nonlinear analysis. Volume 196(2020)
• Publication Date: 2020-07
• Subjects: 35A01 -- 35B40 -- 35B44 -- 35K65; Degenerate parabolic equations -- Global well-posedness -- Asymptotic behavior -- Blow-up -- A family of potential wells; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2020.111759
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: The initial–boundary value problem for a class of degenerate parabolic equations is studied. Some new results on global existence of solutions are established by introducing a family of potential wells. In addition, asymptotic behavior and finite time blow-up of solutions are obtained in the case of subcritical initial energy and critical initial energy, respectively.