Multi-parameters identification problem for a degenerate parabolic equation

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:366

Article

Yang, Liu^1,2  Liu, Yun⁴  Deng, Zui-Cha^1,3 

[1] Lanzhou Jiaotong Univ, Dept Math, Lanzhou 730070, Gansu, Peoples R China

[2] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Gansu, Peoples R China

[3] Lanzhou Jiaotong Univ, Comp Sci & Technol Expt Teaching Ctr, Lanzhou 730070, Gansu, Peoples R China

[4] Tarim Univ, Coll Informat Engn, Alar 843300, Xinjiang, Peoples R China

关键词: Inverse problem;    Initial value;    Source coefficient;    Degenerate parabolic equations;    Conditional stability;    Numerical results;   

DOI  :  10.1016/j.cam.2019.112422

来源: Elsevier

【 摘 要 】

This paper investigates an inverse problem of simultaneously reconstructing the initial value and source coefficient in a degenerate parabolic equation. Problems of this type have important applications in several fields of applied science. Being different from other inverse coefficient problems in classical parabolic equations (non-degenerate), the principal coefficient in the mathematical model discussed in the paper may vanish on both extremities of the domain. On the basis of Carleman estimate, the uniqueness and conditional stability of solution for the original problem are established. Then an iteration algorithm of Landweber type is designed to obtain the numerical solution and some typical numerical experiments are also performed. Numerical results show that the proposed method is stable and the unknown coefficients are recovered quite well. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

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