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.
Citation
Hideo Kubo. Kôji Kubota. "Scattering for systems of semilinear wave equations with different speeds of propagation." Adv. Differential Equations 7 (4) 441 - 468, 2002. https://doi.org/10.57262/ade/1356651803
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