Identification of the unknown diffusion coefficient in a quasi-linear parabolic equation by semigroup approach with mixed boundary conditions

Abstract

In this article, a semigroup approach is presented for the mathematical analysis of the inverse coefficient problems of identifying the unknown diffusion coefficient k(u(x, t)) in the quasi-linear parabolic equation ut (x, t) = (k(u (x, t))u(x) (x, t))(x), with Dirichlet boundary conditions u(x) (0, t) = psi(0), u (1, t) = psi(1). The main purpose of this work is to analyze the distinguishability of the input-output mappings Psi[.]: k -> C(1) [0, T] using semigroup theory. In this article, it is shown that if the null space of semigroups T(t) and S(t) consists of only a zero function, then the input-output mappings Phi[.] and Psi[.] have the distinguishability property. Copyright (c) 2008 John Wiley & Sons, Ltd.