Analytical solution of the problem of gas flow in profiled capillary with vibration of its walls

A mathematical model of gas flow in a profiled capillary with vibration of its walls is made. The analytical solution for functions of pressure and gas flow at usage of asymptotic analysis at infinitely large vibration frequency is obtained. Particular alternate solutions are considered and their agreement with the Poiseuille solution is shown. The comparison of results of analytical solution with the results of numerical one at the finite value of vibration frequency is made.