A generalized quasi-boundary value method for the backward semi-linear time-fractional heat problem in a cylinder |
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Authors: | Mian Liu Chengxin Shi Hao Cheng |
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Institution: | School of Science, Jiangnan University, Wuxi, China |
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Abstract: | 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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Keywords: | backward problem error estimates generalized quasi-boundary value regularization method time-fractional equation |
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