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| Singular Perturbations for Quasilinear Hyperbolic Equations |
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Citation： |
Gao Ruxi.Singular Perturbations for Quasilinear Hyperbolic Equations[J].Chinese Annals of Mathematics B,1983,4(3):293~298 |
| Page view： 790
Net amount： 680 |
Authors： |
Gao Ruxi; |
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| Abstract： |
This paper deals with the following mixed problem for Quasilinear hyperbolic equations
$\[{I_\varepsilon }{u_\varepsilon } \equiv \varepsilon \frac{{{\partial ^2}{u_\varepsilon }}}{{\partial {t^2}}} - \sum\limits_{i,j = 1}^n {{a_{ij}}\frac{{{\partial ^2}{u_\varepsilon }}}{{\partial {x_i}\partial {x_j}}} + {b_0}(t)\frac{{\partial {u_\varepsilon }}}{{\partial t}} + \sum\limits_{i = 1}^n {{b_i}(x,t,{u_\varepsilon }) = f(x,t)} } \] $
$u_\varepsilon|_t=0=\phi(x)$
$\frac{\partial u_\varepsilon}{\partial t}|_t=0=\psi(x)$
$u_\varepsilon|_F=X(x,t)$
The M order uniformly valid asymptotic solutions are obtained and there errors are estimated. |
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