Numerical identification of diffusivity coefficient and initial condition by discrete mollification (Q1905911)

Two inverse problems for parabolic equations are formulated in which the coefficient \(a(x, t)\) and the initial condition \(u(x, 0)\) have to be identified simultaneously under the assumption that the measurements are given at the active boundary only. For each of these problems a stable space marching finite difference scheme based on the mollification method is suggested. Moreover, an error analysis and some interesting numerical exmaples are presented.