Simultaneous Determination of the Space‐Dependent Source and the Initial Distribution in a Heat Equation by Regularizing Fourier Coefficients of the Given Measurements

Shufang Qiu, Wen Zhang and Jianmei Peng

Advances in Mathematical Physics, 2018, vol. 2018, issue 1

Abstract: We consider an inverse problem for simultaneously determining the space‐dependent source and the initial distribution in heat conduction equation. First, we study the ill‐posedness of the inverse problem. Then, we construct a regularization problem to approximate the originally inverse problem and obtain the regularization solutions with their stability and convergence results. Furthermore, convergence rates of the regularized solutions are presented under a prior and a posteriori strategies for selecting regularization parameters. Results of numerical examples show that the proposed regularization method is stable and effective for the considered inverse problem.

Date: 2018
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https://doi.org/10.1155/2018/8247584

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2018:y:2018:i:1:n:8247584

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