The obstacle problem for a fourth order semilinear parabolic equation

Shinya Okabe, Kensuke Yoshizawa

Research output: Contribution to journalArticle

Abstract

This paper is concerned with the obstacle problem for the L2-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.

Original languageEnglish
Article number111902
JournalNonlinear Analysis, Theory, Methods and Applications
Volume198
DOIs
Publication statusPublished - 2020 Sep

Keywords

  • Fourth order semilinear parabolic equation
  • Minimizing movements
  • Obstacle problem

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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