A generalized quasi-boundary value method for the backward semi-linear time-fractional heat problem in a cylinder

We are concerned with a backward problem associated with a semi-linear time-fractional heat equation in an axis-symmetric cylinder, which arises from the modeling of the blast furnace steelmaking in metallurgy. Under some assumptions, the existence and uniqueness of the solution to the semi-linear problem is first established. The ill-posedness of the backward problem is then established, and we obtain the error estimates by a generalized quasi-boundary value regularization method. Finally, the numerical experiment is presented to demonstrate the effectiveness of the proposed method.

Automated summary

This paper investigates a backward problem associated with a semi-linear time-fractional heat equation in an axis-symmetric cylinder, which is motivated by the modeling of blast furnace steelmaking in metallurgy. The existence and uniqueness of the solution to the semi-linear problem are established under certain assumptions. Furthermore, the ill-posedness of the backward problem is proven and error estimates are obtained using a generalized quasi-boundary value regularization method. A numerical experiment is presented to demonstrate the effectiveness of the proposed method.