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

Abstract

The identification of an unknown coefficient in the lower term of elliptic second-order differential equation Mu + ku = f with the boundary condition of the third type is considered. The identification of the coefficient is based on integral boundary data. The local existence and uniqueness of the strong solution for the inverse problem is proved

An Inverse Problem for a Quasilinear Elliptic Equation

“…We use the method developed in [1]- [3] and based on reducing the inverse problem to an operator equation of the second kind for the unknown coefficient [4]. We note that the inverse problem for the linear equation Mu + ku = f with unknown constant coefficient k was studied in [5] and [6] in the case of boundary conditions of the first and third kind respectively.…”