Asymptotic profiles for the Kirchhoff equation

  • TOKIO MATSUYAMA

    Tokai University, Kanagawa, Japan

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.

Cite this article

TOKIO MATSUYAMA, Asymptotic profiles for the Kirchhoff equation. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 17 (2006), no. 4, pp. 377–395

DOI 10.4171/RLM/475