Analysis of a Semigroup Approach in the Inverse Problem of Identifying an Unknown Coefficient

Abstract

This article presents a semigroup approach to the mathematical analysis of the inverse coefficient problems of identifying file Unknown coefficient k(u(x)) in file quasi-linear parabolic equation u(t)(x,t) = (k(u(x))u(x)(x,t))(x) +F(x,t), with Dirichlet boundary conditions u(0,t)=psi(0), u(l,t) = psi(1) and funclion F(x,t). The main purpose of this paper is to investigate the distinguishability of the input-out mappings phi[center dot]:k -> C-1[0,T], psi[center dot]:K -> C-1[0,T] via semigroup theory. Copyright (C) 2008 John Wiley & Sons, Ltd.