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| Global Classical Solution and AsymptoticBehavior to a Kind of Linearly DegenerateQuasilinear Hyperbolic System |
| Changhua Wei,Tiantian Xing |
| (Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou,
Zhejiang 310018, China;
Nanbei Lake Institute for Artificial Intelligence in Medicine, Jiaxing,
Zhejiang 314300, China) |
| DOI： |
| 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 nonlinearties. |
| Key words: Hyperbolic system, linearly degenerate, positive weighted energy estimates,
global existence, asymptotic behavior. |