Asymptotic Behavior of Solutions for a Fourth Order Parabolic Equation with Gradient Nonlinearity via the Galerkin Method

Nobuhito Miyake, Shinya Okabe

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

In this paper we consider the initial-boundary value problem for a fourth order parabolic equation with gradient nonlinearity. The problem is regarded as the L2-gradient flow for an energy functional which is unbounded from below. We first prove the existence and the uniqueness of solutions to the problem via the Galerkin method. Moreover, combining the potential well method with the Galerkin method, we study the asymptotic behavior of global-in-time solutions to the problem.

Original languageEnglish
Title of host publicationSpringer INdAM Series
PublisherSpringer-Verlag Italia s.r.l.
Pages247-271
Number of pages25
DOIs
Publication statusPublished - 2021

Publication series

NameSpringer INdAM Series
Volume47
ISSN (Print)2281-518X
ISSN (Electronic)2281-5198

Keywords

  • Epitaxial growth
  • Fourth order parabolic equation
  • Galerkin method
  • Gradient nonlinearity

ASJC Scopus subject areas

  • Mathematics(all)

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