On the properties of solutions of a nonlinear filtration problem with a source and multiple nonlinearities

In this work, we studied the conditions for global solvability and unsolvability of a nonlinear filtration problem with a source and with a nonlinear boundary flow. The critical exponent of the global existence of the solution and the critical exponent of the Fujita type of the problem of nonlinear filtration in an inhomogeneous medium are established. An asymptotic representation of a compactly supported solution is obtained, which makes it possible to carry out a numerical experiment.