I will discuss an asymptotic completeness result for a scalar quasilinear wave equation in three space dimensions. This equation satisfies the weak null condition introduced by Lindblad and Rodnianski, and it admits small data global existence which was proved by Lindblad. In this talk, I will first introduce a new notion of asymptotic profile by deriving a new reduced system for the model equation. I will then present a proof of the asymptotic completeness. In other words, given a global solution to the model equation, I will show how to find the corresponding asymptotic profile.

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