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

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))ux(x, t))x, with Dirichlet boundary conditions ux(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 (phi)[·] : (kappa)C1[0, T], (psi)[·]:(kappa)(right arrow)[·] C1[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 (kappa)[·] have the distinguishability property.