Identification of the unknown boundary condition in a linear parabolic equation

Abstract

In this article, a semigroup approach is presented for the mathematical analysis of the inverse problems of identifying the unknown boundary condition u(1, t) = f (t) in a linear parabolic equation ut (x, t) = (k(u(x, t))ux(x, t))x with Dirichlet boundary conditions u(0, t) = Ψ0, u(1, t) = f (t) by making use of the over measured data u(x0, t) = Ψ1 and ux(x0, t) = Ψ2 separately. © 2013 Demir and Ozbilge; licensee Springer.