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Global Classical Solution and Asymptotic Behavior to a Kind of Linearly Degenerate Quasilinear Hyperbolic System

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.

Author Details

Changhua Wei

Tiantian Xing