Аңдатпа
The inverse problem for determining the right part of the pseudo-parabolic equationIn this paper the inverse problem of determining a solution and an unknown right-hand side that depends only on spatial variable for the linear pseudo-parabolic equation of the third order is investigated.In inverse problems, together with the initial and boundary conditions also consider an additional information, the need for which is due to the presence of unknown coefficients or the right side of the equation.In this paper, as additional information the integral overdetermination condition is considered.Inverse problems of determining the right-hand side of a differential equation arise in the mathematical modeling of some physical processes in the case when, in addition to solving the equation, it is necessary to restore the action of external sources.Today, studies of direct and inverse problems for pseudo-parabolic equations are rapidly developing due to the needs of modeling and process control in thermophysics, hydrodynamics and continuum mechanics.Similar pseudo-parabolic equations to considered in this paper arise in the description of heat and mass transfer processes, processes of motion of non-Newtonian fluids, wave processes, and in many other areas.Using series expansion, the existence and uniqueness theorems of classical solutions to this problem are proved.The result of this work is a solution presented in the series form, which allows the necessary numerical calculations to be performed with a given accuracy.