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The present work deals with the analysis of the mathematical models of nonlinear filtration problems for an incompressible fluid in an arbitrary bounded domain in the presence of the several point sources. We consider a continuous and a multi valued filtration laws. We assume that the function determining the filtration law has a linear growth at infinity. The problems are stated mathematically as an equation (in the case of a continuous filtration law) or as variational inequality of the second kind (in the case of a multi valued filtration law) in a Hilbert space. For the solving the mentioned problems the iterative processes are offered. The results of numerical experiments the effectiveness of these methods are confirmed.
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