Advances in Differential Equations

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

Hideo Kubo and Kôji Kubota

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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

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

First available in Project Euclid: 27 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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.

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