| GLOBAL CLASSICAL SOLUTIONS TO QUASILINEAR HYPERBOLIC SYSTEMS WITH WEAK LINEAR DEGENERACY |
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| 作者姓名： | ZHOU Yi |
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| 作者单位： | ZHOU Yi InstituteofMathematics，FudanUniversity，Shanghai200433，China. |
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| 基金项目： | Project supported by the National Natural Science Foundation of China (No.10225102)，the 973 Project of the Ministry of Science and Technology of China and the Doctoral Programme Foundation of the Ministry of Education of China. |
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| 摘 要： | §1. Introduction and Main Results Consider the following ?rst order quasilinear strictly hyperbolic system ?u ?u A(u) = 0, (1.1) ?t ?xwhere u = (u1, ···,un)T is the unknown vector function of (t,x) and A(u) is an n×n matrixwith suitably smooth elements aij(u) (i,j = 1, ···,n). By the de?nition …
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| 关 键 词： | 全局经典解 拟线性双曲系统 弱线性退化 Cauchy问题 |
| 收稿时间： | 4/3/2023 12:00:00 AM |
| 修稿时间： | 9/3/2003 12:00:00 AM |
GLOBAL CLASSICAL SOLUTIONS TO QUASILINEAR HYPERBOLIC SYSTEMS WITH WEAK LINEAR DEGENERACY |
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| ZHOU Yi.GLOBAL CLASSICAL SOLUTIONS TO QUASILINEAR HYPERBOLIC SYSTEMS WITH WEAK LINEAR DEGENERACY[J].Chinese Annals of Mathematics,Series B,2004,25(1):37-56. |
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| Authors: | ZHOU Yi |
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| Institution: | Institute of Mathematics, Fudan University, Shanghai 200433, China |
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| Abstract: | Consider the following Cauchy problem for the first order quasilinear strictly hyperbolic system θu/θt+A(u)θu/θx=0.t=0:u=f(x).We let M=supx∈R│f'(x)│<+∞.The main result of this paper is that under the assumption that the system is weakly linearly degenerated, there exists a positive constant e independent of M, such that the above Cauchy problem admits a unique global C1 solution u = u(t, x) for all t ∈ R,provided that ∫+∞-∞│f'(x)│dx<-∈,∫+∞-∞│f'(x)│dx<-∈/M. |
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| Keywords: | Global classical solutions Cauchy problems Weak linear degeneracy |
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