ASYMPTOTICS OF THE SOLUTION OF ONE SINGULARLY PERTURBED HYPERBOLIC EQUATION
The singularly perturbed quasilinear hyperbolic equations are considered. The existence of the solutions of moving front type, having contrast structure is proved. The asymptotic expansion of the moving interior layer solution is built based on the boundary layer function method. The equation for moving front velocity was obtained. Important case of quasi-discrete nonlinearities was considered.