Dynamics of Partial Differential Equations

Volume 19 (2022)

Number 4

Asymptotic behavior of global solutions to some multidimensional quasilinear hyperbolic systems

Pages: 273 – 284

DOI: https://dx.doi.org/10.4310/DPDE.2022.v19.n4.a2

Authors

Dongbing Zha (Dongbing Zha, Department of Mathematics, Donghua University, Shanghai, China)

Minghui Sun (Minghui Sun, Department of Mathematics, Donghua University, Shanghai, China)

Abstract

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 [13]. 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.

Keywords

quasilinear hyperbolic systems, scattering problem, rigidity

2010 Mathematics Subject Classification

Primary 35L40. Secondary 35L60.

Full Text (PDF format)

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