Dynamics of Partial Differential Equations
Volume 18 (2021)
Asymptotic behavior of global solutions to one-dimension quasilinear wave equations
Pages: 81 – 100
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.
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