New Trends in the Theory of Hyperbolic Equations pp 113-211 | Cite as

# On the Global Behavior of Classical Solutions to Coupled Systems of Semilinear Wave Equations

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## Abstract

The aim of this work is twofold. One is to develop an approach for dealing with semilinear wave equations adopted by John [38]. In Section 2, the basis of the argument will be explained in a self-contained way. The other is an application of the approach to systems of wave equations. We shall make use of it to handle the semilinear case in Sections 3,4 and 5, and to consider the quasilinear case in Section 6. In these argument we bring such systems that the single wave components obey different propagation speeds into focus.

## Keywords

Nonlinear hyperbolic systems global solutions blow-up lifespan self-similar solutions asymptotic behavior## Preview

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