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(t)(x, t) = u(xx)(x, t) + a(x, t)u(x, t) with Dirichlet boundary conditions u(0, t) = psi(0), u(1, t) = psi(1). It is shown that the unknown coefficient a(x, t) can be approximately determined via the semigroup approach.