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

Yoshiyuki Kagei, Yasunori Maekawa

Research output: Contribution to journalArticle

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 - May 15 2011

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Asymptotic Profile
Self-similar Solutions
Asymptotic Behavior of Solutions
Evolution Equation
Invariance
Scaling
Precise Asymptotics
Invariant
Nonlinear Evolution Equations
General Solution
Class
Framework

All Science Journal Classification (ASJC) codes

  • Analysis

Cite this

Asymptotic behaviors of solutions to evolution equations in the presence of translation and scaling invariance. / Kagei, Yoshiyuki; Maekawa, Yasunori.

In: Journal of Functional Analysis, Vol. 260, No. 10, 15.05.2011, p. 3036-3096.

Research output: Contribution to journalArticle

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