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

作　　者：Changhua Wei Tiantian Xing 

机构地区：[1]Department of Mathematics,Zhejiang Sci-Tech University,Hangzhou,Zhejiang 310018,China [2]Nanbei Lake Institute for Artificial Intelligence in Medicine,Jiacing,Zhejiang 314300,China

出　　处：《Annals of Applied Mathematics》2024年第3期314-332,共19页应用数学年刊（英文版）

基　　金：partially supported by the Outstanding Youth Fund of Zhejiang Province (Grant No. LR22A010004);the NSFC (Grant No. 12071435)。

摘　　要：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.

关 键 词：Hyperbolic system linearly degenerate positive weighted energy estimates global existence asymptotic behavior 

分 类 号：O175.27[理学—数学]