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

Nobuhito Miyake, Shinya Okabe

研究成果: Chapter

抄録

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.

本文言語English
ホスト出版物のタイトルSpringer INdAM Series
出版社Springer-Verlag Italia s.r.l.
ページ247-271
ページ数25
DOI
出版ステータスPublished - 2021

出版物シリーズ

名前Springer INdAM Series
47
ISSN(印刷版)2281-518X
ISSN(電子版)2281-5198

ASJC Scopus subject areas

  • 数学 (全般)

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