The asymptotic problems of filtration with phase transitions

The multi-component two-phase filtration flow has been considered. The production process is characterized with the low depression. Besides there is a small parameter determined with the ratio of the densities and viscosity coefficients. The small parameter system is a singularly perturbed one. As a result of the investigation it is established the self-similar regime near the well with a maximal possible value of the gas saturation has been formed during the short time. The theory of the singularly perturbed equations had resulted in the existence of the boundary layers both in the space and the time domain where the flow is not self-similar one.