Determination of an 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))u x(x,t))x, with Dirichlet boundary conditions u(0,t)=?0, u(1,t)=f(t) by making use of the over measured data u(x0,t)=?1 and ux(x0,t)= ?2 seperately. © 2010 American Institute of Physics.