|
|
| |
| Global Smooth Solutions of Dissipative Boundary Value Problems for First Order Quasilinear Hyperbolic Systems |
| |
Citation： |
Qin Tiehu.Global Smooth Solutions of Dissipative Boundary Value Problems for First Order Quasilinear Hyperbolic Systems[J].Chinese Annals of Mathematics B,1985,6(3):289~298 |
| Page view： 918
Net amount： 889 |
Authors： |
Qin Tiehu; |
|
|
| Abstract： |
This paper discusses the following initial-boundary value problems for the first order quasilinear hyperbolic systems:
$\frac{\partial u}{\partial t}+A(u)\frac{\partial u}{\partial x}=0,$(1)
$u^II=F(u^I),as x=0,$(2)
$u^I=G(u^II),as x=L,$(3)
$u=u^0(x),as t=0,$(4)
where the boundary conditions (2), (3) satisfy F(0) =0, G(0)=0 and the dissipative conditions, that is, the spectral radii of matrices $B_1=\frac{\partial F}{\partial u^I}(0)\frac{\partial G}{\partial u^II(0)}$ and $B_2=\frac{\partial G}{\partial u^II(0)\frac{\partial F}{\partial u^I}(0)$ are less than unit.
Under certain assumptions it is proved that the initial-boundary problem (1)—(4) admits a unique global smooth solution u(x,t)and theC^1-norm|u(t)|_\sigma^2 of u(x, t) decays exponentially to zero as t\rightarrrow \infinity provided that the C^I-norm|u^0|_\sigma^1 of the initial data is sufficiently small. |
Keywords： |
|
Classification： |
|
|
|
Download PDF Full-Text
|
|
|
|
