Inverse problems for the stationary and pseudoparabolic equations of diffusion

Abstract

The identification of an unknown coefficient in the lower term of pseudoparabolic differential equation of diffusion (u + ηM u)t + M u + ku = f and elliptic second order differential equation M u + ku = f with the Dirichlet boundary condition is considered. The identification of k is based on an integral boundary data. The local existence and uniqueness of generalized strong solutions for the inverse problems are proved. The stability estimates are exposed.

An inverse problem of identifying the time‐dependent potential in a fourth‐order pseudo‐parabolic equation from additional condition

“…The inverse problems unknown coefficients of pseudo-parabolic equations have been investigated relatively little. For example, inverse problem of identifying the unknown space-dependent coefficient [1], time-dependent coefficients under the integral overdetermination condition [15], integral boundary data [19,21], space-dependent right-hand side under integral condition [17], velocity field, pressure and right-hand side with additional condition as an integral overdetermination condition [16]. Yaman and Gözükizil [31] studied it for the asymptotic behavior of the solutions of unknown source term with the integral condition.…”

On an Inverse Problem for the Stationary Equation with a Boundary Condition of the Third Type

“…Following the idea given in [1][2][3] and using method developed in [4], we prove the existence of the solution by reducing the inverse problem to an operator equation of the second kind for the unknown coefficient. Note that the problem for the same equation with Dirichlet boundary conditions was considered [5].…”

The Regularity of the Solutions of Inverse Problems for the Pseudoparabolic Equation

“…In this paper by the regularity of the solution is meant its continuous dependence on the input data of the inverse problem. The regularity of solution, as used here, was established for the inverse problem of finding an unknown lower coefficient g = g(t) in equation (0.1) [7].…”