Dynamics of Partial Differential Equations

Volume 18 (2021)

Number 2

Asymptotic behavior of global solutions to one-dimension quasilinear wave equations

Pages: 81 – 100

DOI: https://dx.doi.org/10.4310/DPDE.2021.v18.n2.a1

Author

Mengni Li (Department of Mathematics and Yau Mathematical Sciences Center, Tsinghua University, Beijing, China)

Abstract

The asymptotic behavior of solutions is a significant subject in the theory of wave equations. In this paper we are concerned with the asymptotic behavior of the unique global solution to the Cauchy problem for one-dimension quasilinear wave equations with null conditions. By applying the small-data-global-existence result and exploiting the strength of weights, we not only provide sharper convergence from the quasilinear case to the linear case but also study the rigidity aspect of the scattering problem for quasilinear waves.

Keywords

quasilinear wave equation, null condition, weight function, asymptotic behavior

2010 Mathematics Subject Classification

Primary 35L05. Secondary 35B40, 35L72.

Received 25 November 2020

Published 10 May 2021