Asymptotics and stability of non-linear parametric oscillations of a singularly perturbed telegraph equation

The solution of the problem indicated in the title is based on the method of quasi-normal forms developed previously by the author for the construction of stationary regimes of parabolic systems with small diffusion. As in the parabolic case, it relies on the theory of exponential dichotomy of solutions and on an algorithm in the study of stability of linear differential equations whose coefficients are nearly independent of the time.