Mathematics & Physics 2017, 10(1), 4–15 УДК 517.95 The Inverse Problem for the Nonlinear Pseudoparabolic Equation of Filtration Type Anna Sh. <...> Lyubanova∗ Institute of Space and Information Technologies Siberian Federal University Svobodny, 79, Krasnoyarsk, 660041 Russia Received 25.06.2016, received in revised form 10.09.2016, accepted 20.11.2016 The paper discusses the correctness of the inverse problem on finding an unknown coefficient dependent on t in the nonlinear pseudoparabolic equation of the third order with an additional information on the boundary. <...> The existence and uniqueness theorem is proven. <...> The proof of the theorem is carried out by the reduction of the original inverse problem to the equivalent one with an operator equation for the unknown coefficient. <...> Keywords: local existence and uniqueness theorem, a priori estimate, inverse problem, nonlinear higherorder equation, pseudoparabolic equation, filtration. <...> Introduction This paper is devoted to the inverse problems of the identification of coefficients in the pseudoparabolic equation (u+L1u)t +L2u = f, (0.1) with the differential operators L1 and L2 of even order with respect to spacial variables. <...> Such equations arises in the models of the heat transfer, filtration in the fissured media, quasistationary processes in the crystalline semiconductor (see more detailed review in [10, 11]). <...> The first result [9] refers to the inverse problems of determining a source function f in (0.1) with linear operators L1 and L2 of the second order, L1 = L2. <...> In [4], the solvability is established for two inverse problems of recovering the unknown coefficients in terms u (the lowest term of L2u) and ut of (0.1). <...> Here M is a second order linear differential operator in the space variables. <...> In the present article we establish solvability and uniqueness of solutions to the inverse problem of finding an unknown coefficient k = k(t) in the nonlinear equation (0.2) with the use of an additional information on the boundary (see (1.1)–(1.4)). ∗lubanova@mail.ru ⃝ Siberian Federal University. <...> Lyubanova The Inverse Problem for the Nonlinear Pseudoparabolic Equation of Filtration Type 1. <...> Statement of the problem and preliminary results Let Ω be a bounded domain in Rn with a boundary ∂Ω ∈ C2, T is an arbitrary real number following notation: ∥ · ∥ and (·, ·) are the norm and the inner product of L2(Ω); ∥ · ∥j and ⟨·, ·⟩ are the norm of Wj LetM :W1 m(x)I <...>