Asymptotic behavior of global solutions to one-dimension quasilinear wave equations
type: Item
instance of: scholarly article
title: Asymptotic behavior of global solutions to one-dimension quasilinear wave equations
zbMATH Open document ID: 1472.35244
author: Mengni Li
published in: Dynamics of Partial Differential Equations
publication date: 2021-06-11T00:00:00Z
review text: 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.
reviewed by: Dongbing Zha
Mathematics Subject Classification ID: 35L72
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35L52
zbMATH DE Number: 7357832
zbMATH Keywords: null condition
zbMATH Keywords: weight function
zbMATH Keywords: small data setting
Wikidata QID: Q115203651
MaRDI profile type: Publication
full work available at URL: dpde.2021.v18.n2.a1
OpenAlex ID: W3162380447
DOI: 10.4310/DPDE.2021.V18.N2.A1
description: scientific article; zbMATH DE number 7357832