Determination of a control parameter in a parabolic partial differential equation

Abstract

The authors consider in this paper the inverse problem of finding a pair of functions ( u, p ) such that where F, f, E, s , α i , β i , γ i , g i , i = 1, 2, are given functions. The existence and uniqueness of a smooth global solution pair ( u, p ) which depends continuously upon the data are demonstrated under certain assumptions on the data.