The obstacle problem for a fourth order semilinear parabolic equation. (September 2020)

• Record Type: Journal Article
• Authors: Okabe, Shinya; Yoshizawa, Kensuke
• Is Part Of: Nonlinear analysis. Volume 198(2020)
• Publication Date: 2020-09
• Subjects: 35K25 -- 35K86 -- 49J40 -- 74H20 -- 35B44; Obstacle problem -- Fourth order semilinear parabolic equation -- Minimizing movements; 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.2020.111902
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This paper is concerned with the obstacle problem for the L 2 -gradient flow for a functional which is higher order, non-convex and unbounded from below. We prove (i) the existence and uniqueness of local-in-time solutions to the obstacle problem and (ii) a gradient structure of the functional of the solutions, via minimizing movements. Moreover, we show the existence of solutions which blow up in a finite time.