| Abstract: | The exact solutions of the nonlinear equations of filtration of an aerated liquid have been obtained in 1–3]. In 4] the system of equations of an aerated liquid have been reduced to the heat-conduction equation under certain assumptions. An approximate method of computing the nonsteady flow of an aerated liquid is given in 5], where the real flow pattern is replaced by a computational scheme of successive change of stationary states. In 6] the same problem is solved by the method of averaging. In the present article estimates of the solution of the equations for nonstationary filtration of an aerated liquid in one-dimensional layer are constructed under certain conditions imposed on the desired functions. These estimates can be used as approximate solutions with known error or for the verification of the accuracy of different approximate methods. We note that the use of comparison theorem for the estimate of solutions of equations of nonlinear filtration is discussed in 7–9]. The methods of constructing estimates of solutions of various problems of heat conduction are given in 10, 11] |
