## Differential and Integral Equations

### Scattering and self-similar solutions for the nonlinear wave equation

Kunio Hidano

#### Abstract

We study scattering theory and self-similar solutions for the nonlinear wave equation $\Box u+\lambda|u|^{p-1}u=0$ in two or three space dimensions under the assumption $p_0(n) <p <1+4/(n-1)$, where $p_0(n)$ is the larger root of the equation $(n-1)p^2-(n+1)p-2=0$. The relation between the theory of scattering and that of self-similar solutions is considered from the point of view of asymptotically free solutions and asymptotically self-similar solutions.

#### Article information

Source
Differential Integral Equations, Volume 15, Number 4 (2002), 405-462.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060843

Mathematical Reviews number (MathSciNet)
MR1870420

Zentralblatt MATH identifier
1011.35088

Subjects
Primary: 35L70: Nonlinear second-order hyperbolic equations
Secondary: 35B40: Asymptotic behavior of solutions

#### Citation

Hidano, Kunio. Scattering and self-similar solutions for the nonlinear wave equation. Differential Integral Equations 15 (2002), no. 4, 405--462. https://projecteuclid.org/euclid.die/1356060843