An inverse problem for a time-fractional advection equation associated with a nonlinear reaction term

Vo, Hoang-Hung; Minh, Triet Le; Hong, Phong Luu; Van, Canh Vo

doi:10.1080/17415977.2020.1849183

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“…In previous studies, [23][24][25][26] the authors obtained the solution of backward problem of the one-dimensional time-fractional heat equation. Vo et al 27 solved the backward problem of the two-dimensional semi-linear time-fractional heat equation.…”

Section: Introductionmentioning

confidence: 99%

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

Liu

Shi

Cheng

2022

Math Methods in App Sciences

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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.

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