Asymptotic behaviors of solutions to evolution equations in the presence of translation and scaling invariance

Yoshiyuki Kagei, Yasunori Maekawa

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

There are wide classes of nonlinear evolution equations which possess invariant properties with respect to a scaling and translations. If a solution is invariant under the scaling then it is called a self-similar solution, which is a candidate for the asymptotic profile of general solutions at large time. In this paper we establish an abstract framework to find more precise asymptotic profiles by shifting self-similar solutions suitably.

Original languageEnglish
Pages (from-to)3036-3096
Number of pages61
JournalJournal of Functional Analysis
Volume260
Issue number10
DOIs
Publication statusPublished - 2011 May 15

Keywords

  • Evolution equations
  • Large time behaviors of solutions
  • Self-similar solutions

ASJC Scopus subject areas

  • Analysis

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