Identification of the Unknown Coefficient in a Quasi-Linear Parabolic Equation by a Semigroup Approach

Abstract

This article presents a semigroup approach to the mathematical analysis of the inverse coefficient problems of identifying the unknown coefficient a(x, t) in the quasi-linear parabolic equation u<inf>t</inf>(x, t) = u<inf>xx</inf>(x, t) + a(x, t)u(x, t) with Dirichlet boundary conditions u(0, t) = ψ<inf>0</inf>, u(1, t) = ψ<inf>1</inf>. It is shown that the unknown coefficient a(x, t) can be approximately determined via the semigroup approach. © 2013 Ozbilge and Demir. © 2014 Elsevier B.V., All rights reserved.