TY - JOUR
T1 - Global Classical Solution and Asymptotic Behavior to a Kind of Linearly Degenerate Quasilinear Hyperbolic System
AU - Wei , Changhua
AU - Xing , Tiantian
JO - Annals of Applied Mathematics
VL - 3
SP - 314
EP - 332
PY - 2024
DA - 2024/09
SN - 40
DO - http://doi.org/10.4208/aam.OA-2024-0017
UR - https://global-sci.org/intro/article_detail/aam/23425.html
KW - Hyperbolic system, linearly degenerate, positive weighted energy estimates,
global existence, asymptotic behavior.
AB - <p style="text-align: justify;">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.</p>