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| STABILITY OF GLOBAL GEVREY SOLUTION TO WEAKLY HYPERBOLICEQUATIONS |
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Citation： |
M. Reissig,K. Yagdjian.STABILITY OF GLOBAL GEVREY SOLUTION TO WEAKLY HYPERBOLICEQUATIONS[J].Chinese Annals of Mathematics B,1997,18(1):1~14 |
| Page view： 1033
Net amount： 844 |
Authors： |
M. Reissig; K. Yagdjian |
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| Abstract： |
This work is concerned with the proof of stability of global Gevrey solution
to the following quasilinear weakly hyperbolic equation:
$u_{tt}-a(x,t)u_{xx}=f(x,t,u,u_x)$ in $P \times [0,T]$ with initial data
$u(x,0)=u_0(x)$ and $u_t(x,0)=u_1(x)$. Here weak hyperbolicity means that
$a(x,t) \ge 0$, that is, there exist, in general, characteristic roots of
variable multiplicity. One has to distinguish between the case of spatial
degeneracy and that of time degeneracy. The connection to the life span
of solutions is given. |
Keywords： |
Quasilinear weakly hyperbolic equations, Gevrey functions,
Global solvability,Stability, Life span of solutions |
Classification： |
35L70, 35L80, 35B20 |
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