SINGULAR PERTURBATIONS FOR QUASILINEAR HYPERBOLIC EQUATIONS

This paper deals with the following mixed problem for Quasilinear hyperbolic equationsThe M order uniformly valid asymptotic solutions are obtained and there errors areestimated.

Singular Perturbations for Quasilinear Hyperbolic Equations

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.