Simultaneous Reconstructions of (x,t) -Dependent Coefficients and Initial Conditions of Parabolic Equations
This work investigates reconstructing both an unknown coefficient that changes with space and time and an unknown initial condition for a general linear parabolic equation. The researchers developed new H"older stability estimates for the coefficient and a logarithmic stability estimate for the initial condition, proving uniqueness for both unknowns. This is significant as it advances methods beyond previous limitations on how these problems are studied.