Dynamics of Partial Differential Equations
Volume 19 (2022)
Asymptotic behavior of global solutions to some multidimensional quasilinear hyperbolic systems
Pages: 273 – 284
For the Cauchy problem of multidimensional quasilinear hyperbolic systems of diagonal form without self-interaction, the global existence of classical solutions with small initial data was shown in . In this paper, we will first prove that the global solution will scatter to free linear waves in some weighted $L^p$ sense, then based on it, we will study the rigidity aspect of scattering problem for quasilinear waves.
quasilinear hyperbolic systems, scattering problem, rigidity
2010 Mathematics Subject Classification
Primary 35L40. Secondary 35L60.
The first author is supported by the Fundamental Research Funds for the Central Universities (No. 2232022D–27) and National Natural Science Foundation of China (No.11801068).
Received 1 November 2021
Published 14 December 2022