Advances in Differential Equations

Scattering for systems of semilinear wave equations with different speeds of propagation

Hideo Kubo and Kôji Kubota

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We give an extension of the a priori estimate, obtained in [8], for a solution of the inhomogeneous wave equation in ${\bf R}^n\times{\bf R}$, where $n=2$ or $n=3$. As an application, we study the asymptotic behavior as $t \to \pm \infty$ of solutions to systems of semilinear wave equations. The discrepancy of the speeds of propagation may make a significant difference from the case of common propagation speeds. (See also Theorem 3.3 and 3.4). Whether such a phenomenon occurs or not depends on the type of the interaction determined by the nonlinearities.

Article information

Source
Adv. Differential Equations Volume 7, Number 4 (2002), 441-468.

Dates
First available in Project Euclid: 27 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1356651803

Mathematical Reviews number (MathSciNet)
MR1869119

Zentralblatt MATH identifier
1223.35232

Subjects
Primary: 35L70: Nonlinear second-order hyperbolic equations
Secondary: 35B40: Asymptotic behavior of solutions 35B45: A priori estimates

Citation

Kubo, Hideo; Kubota, Kôji. Scattering for systems of semilinear wave equations with different speeds of propagation. Adv. Differential Equations 7 (2002), no. 4, 441--468. https://projecteuclid.org/euclid.ade/1356651803.


Export citation