Liu Yang

TL;DR: In this paper, the existence and necessary condition of the minimum for the control functional are established based on the optimal control framework, and an algorithm and some numerical experiments are proposed in the paper.

TL;DR: A numerical algorithm on the basis of the Landweber iteration is designed to deal with the operator equation and some typical numerical experiments are performed, showing that the proposed method is stable and the unknown heat source is recovered very well.

TL;DR: In this article, the authors use an optimal control framework to discuss an inverse problem of determining the implied volatility when the average option premium, namely the average value of option premium corresponding with a fixed strike price and all possible maturities from the current time to a chosen future time, is known.

TL;DR: This work investigates the inverse problem of reconstructing a spacewise dependent heat source in the parabolic heat equation using a final temperature measurement and the existence and necessary condition of the minimizer for the cost functional are established.

TL;DR: In this paper, the authors dealt with the determination of a pair (q, u) in the heat conduction equation with initial and boundary conditions from the overspecified data u(x, t) = g(x and t).