Asymptotic behavior of global solutions to one-dimension quasilinear wave equations
In this paper, the author considered the Cauchy problem of one-dimension systems of quasilinear wave equations with null conditions. In the small data setting, based on the global existence results in [\textit{G. K. Luli} et al., Adv. Math. 329, 174--188 (2018; Zbl 1392.35190)] in the semilinear case, and [\textit{D. Zha}, Calc. Var. Partial Differ. Equ. 59, No. 3, Paper No. 94, 19 p. (2020; Zbl 1441.35176)] in the quasilinear case, she gave some further asymptotic behavior results for the global solution. First, she showed that the global solution is asymptotically free in the weighted energy sense. This result generalized the corresponding one in [loc. cit.], which gave the global solution is asymptotically free in the unweighted energy sense. Then, she showed the rigidity of the scattering field.
scientific article; zbMATH DE number 7357832