Mathematics & Physics 2015, 8(4), 467–477 УДК 517.9 Localization of Solutions of the Equations of Filtration in Poroelastic Medium Margarita A.Tokareva∗ Faculty of Mathematics and Information Technologies Altai State University Lenina, 61, Barnaul, 656049 Russia Received 22.06.2015, received in revised form 10.08.2015, accepted 20.09.2015 A system of equations of 1D non-stationary fluid motion in poroelastic medium is considered. <...> Localization of solutions of the equations has been established by the integral energy estimates method. <...> This quasi-linear system of equations describes 1D non-stationary isothermal motion of fluid in poroelastic medium. <...> The laws of conservation of mass for each phase, Darcy’s law for fluid phase, the rheological Maxwell law and the equation of conservation of momentum for the system describe this process. <...> Here ρs, ρf , vs, vf are, respectively, real density and velocity of solid and fluid phases, φ is the porosity, pf , ps are, respectively, pressures of the fluid and solid phases; pe is the effective pressure, ptot is the total pressure, ρtot is the density of the two-phase medium, g is the density of the mass forces, k(φ) is the coefficient of filtration, βt(φ) is the coefficient of bulk compressibility (specified function). <...> The problem is written in the Eulerian coordinates x, t. The real density of the fluid and solid particles ρf , ρs are assumed constant. <...> The unknown quantities are φ, vs, vf , pf , ps. Local (with respect to time) solvability of the initial-boundary value problem for the system of equations under consideration has been established in [4], a self-similar solution has been ∗tma25@mail.ru ⃝ Siberian Federal University. <...> All rights reserved c – 467 – (∂pf ∂x −ρfg ∂pe ∂x ∂t + ∂ ) , ) , ∂x(ρfφvf ) = 0, Margarita A.Tokareva Localization of Solutions of the Equations of Filtration in Poroelastic Medium found in [5]. <...> Numerical results for this system of equations are given in [1, 2]. <...> In these studies we use Euler variables, additional assumptions about smallness of the speed of solid phase, and the following relations between the functional parameters of the problem: k(φ) = k µφn, βt(φ) = βφφb, where n, b are positive environment parameters. <...> This system <...>