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

Yoshiyuki Kagei; Yasunori Maekawa

doi:10.1016/j.jfa.2011.02.004

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

Yoshiyuki Kagei, Yasunori Maekawa

SCI - Mathematics

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	3036-3096
Number of pages	61
Journal	Journal of Functional Analysis
Volume	260
Issue number	10
DOIs	https://doi.org/10.1016/j.jfa.2011.02.004
Publication status	Published - 2011 May 15

Keywords

Evolution equations
Large time behaviors of solutions
Self-similar solutions

ASJC Scopus subject areas

Analysis

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10.1016/j.jfa.2011.02.004

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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.",

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KW - Self-similar solutions

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