On the asymptotics of the Goursat problem with a power boundary layer

In this paper, we consider the Goursat problem for a partial differential equation containing a small parameter $\varepsilon$ in the coefficient of the highest derivative. For $\varepsilon=0$, the order of the equation does not decrease, but a singularity appears, which has the nature of a power boundary layer. A solution of the singularly perturbed Gaussian problem is constructed in the form of a formal series in powers of the small parameter. The asymptotic nature of the constructed series is proved.