JournalsrlmVol. 17 , No. 4DOI 10.4171/rlm/475

Asymptotic profiles for the Kirchhoff equation

  • TOKIO MATSUYAMA

    Tokai University, Kanagawa, Japan
Asymptotic profiles for the Kirchhoff equation cover

Abstract

The first aim of this paper is to find asymptotic profiles for Kirchhoff equation. More precisely, it will be shown that there exists a small amplitude solution which is not asymptotically free. The second aim is to prove the existence of scattering states for the small amplitude solutions with data belonging to Hσ(p),p×Hσ(p)1,pH^{\sigma(p),p}\times H^{\sigma(p)-1,p}, where σ(p)=n(2p1)+1\sigma(p)= n(\frac{2}{p}-1)+1, p[1,2(n1)n+1)p\in [1,\frac{2(n-1)}{n+1}) and n4n \ge 4.