Global Classical Solution and Asymptotic Behavior to a Kind of Linearly Degenerate Quasilinear Hyperbolic System
Year: 2024
Author: Changhua Wei, Tiantian Xing
Annals of Applied Mathematics, Vol. 40 (2024), Iss. 3 : pp. 314–332
Abstract
This paper is concerned with the global classical solution and the asymptotic behavior to a kind of linearly degenerate quasilinear hyperbolic system in several space variables. When the semilinear terms contain at least two waves with different propagation speeds, we can prove that the system considered admits a global classical solution by the weighted energy estimate under the small and suitable decay assumptions on the initial data. Furthermore, we can show that the solution converges to a solution of the linearized system based on the decay property of the nonlinearities.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aam.OA-2024-0017
Annals of Applied Mathematics, Vol. 40 (2024), Iss. 3 : pp. 314–332
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Hyperbolic system linearly degenerate positive weighted energy estimates global existence asymptotic behavior.