On Solvability of An Inverse Boundary Value Problem For The Elliptic Equation Of Second Order With Periodic And Integral Condition
Abstract
An inverse boundary value problem for a
second-order elliptic equation with periodic and integral condition is
investigated. The definition of a classical solution of the problem is
introduced. The goal of this paper is to determine the unknown coefficient and
to solve the problem of interest. The problem is considered in a rectangular
domain. To investigate the solvability of the inverse problem, we perform a
conversion from the original problem to some auxiliary inverse problem with
trivial boundary conditions. By the contraction mapping principle we prove the
existence and uniqueness of solutions of the auxiliary problem. Then we make a
conversion to the stated problem again and, as a result, we obtain the
solvability of the inverse problem.
Keywords
Fourier method,Inverse boundary value problem,Elliptic equation,Classical solution.
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