On the uniqueness of solution Cauchy's inverse problem for the equation Δu=au+b

Abstract

The inverse Cauchy problem Δu(x) = au(x) + b 0f orx ∈ ω ,a ndu = 0, ∂u = Φ on γ is shown as having a unique solution within a wide class of simply connected domains ω R 2 with smooth boundary γ .H ere a and b are real numbers to be determined, and Φ is a given function which is normalized by the condition � γ Φ ds = 1.