Some extended results on a nonlinear ill-posed heat equation and remarks on a general case of nonlinear terms |
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| Authors: | Nguyen Huy Tuan Pham Hoang Quan |
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| Affiliation: | 1. Institute for Computational Science and Technology HoChiMinh City, Quarter 6, Linh Trung Ward, Thu Duc District, HoChiMinh City, Viet Nam;2. Department of Mathematics, Hochiminh University of Technology, 144/24 Dien Bien Phu, P.25, Binh Thanh District, Hochiminh city, Viet Nam;3. Department of Mathematics and Applications, Sai Gon University, 273 An Duong Vuong, Q.5, HoChiMinh City, Viet Nam |
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| Abstract: | The major object of this paper is to provide a quite convenient regularization method for a nonlinear backward heat problem. Error estimates for this method are provided together with a selection rule for the regularization parameter. Our method improve some results in a previous paper, including the earlier paper [D.D. Trong, N.H. Tuan, Regularization and error estimate for the nonlinear backward heat problem using a method of integral equation, Nonlinear Anal. 71 (9) (2009) 4167–4176] and some other papers. A general case of nonlinear terms for this problem is obtained. |
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