Analysis for the identification of an unknown diffusioncoefficient via semigroup approach

摘要

This paper presents a semigroup approach for the mathematical analysis of the inverse coefficient problemsof identifying the unknown coefficient k(u_x) in the inhomogenenous quasi-linear parabolic equationu_t(x,t)=(k(u_x)u_x(x,t))_x+F(u), with the Dirichlet boundary conditions u(0,t)=ψ_0,u(1,t)=ψ_1 andsource function F(u). The main purpose of this paper is to investigate the distinguishability of the input output mappings (14[]:://r—> CI [0, T],511[.]:,7i—* CI [0, T] via semigroup theory.