Identification of a constant coefficient in an elliptic equation

Abstract

The identification of an unknown constant coefficient in the main term of elliptic second order differential equation kMu + g(x)u = f(x) with the Dirichlet boundary condition is considered. The elliptic operator M is self-adjoint and bounded in . The identification of k here is based on an integral boundary data. The local existence and uniqueness theorem for the inverse problem is proved in the class of the pairs involving a function and a positive real number k. The uniqueness is obtained by a new approach.

Keywords:

• inverse problems for PDE
• boundary value problems for second-order elliptic equations
• local existence and uniqueness theorems
• filtration

AMS Subject Classifications: :

• 35R30
• 35J25
• 35A07
• 76S05