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Volume 28, Issue 4
Semi-discretization Difference Approximation for a Cauchy Problem of Heat Equation in Two-dimensional Space

Xiangtuan Xiong & Jinmei Li

DOI: 10.4208/jpde.v28.n4.3

J. Part. Diff. Eq., 28 (2015), pp. 315-331.

Published online: 2015-12

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  • Abstract
In this paper we consider a semi-descretization difference scheme for solving a Cauchy problem of heat equation in two-dimensional setting. Some error estimates are proved for the semi-descretization difference regularization method which cannot be fitted into the framework of regularization theory presented by Engl, Hanke and Neubauer. Numerical results show that the proposed method works well.
  • Keywords

2D inverse heat conduction problem Ill-posedness regularization error estimate finite difference

  • AMS Subject Headings

65R35

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

xiongxt@gmail.com (Xiangtuan Xiong)

992461300@qq.com (Jinmei Li)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-28-315, author = {Xiong , Xiangtuan and Li , Jinmei}, title = {Semi-discretization Difference Approximation for a Cauchy Problem of Heat Equation in Two-dimensional Space}, journal = {Journal of Partial Differential Equations}, year = {2015}, volume = {28}, number = {4}, pages = {315--331}, abstract = { In this paper we consider a semi-descretization difference scheme for solving a Cauchy problem of heat equation in two-dimensional setting. Some error estimates are proved for the semi-descretization difference regularization method which cannot be fitted into the framework of regularization theory presented by Engl, Hanke and Neubauer. Numerical results show that the proposed method works well.}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v28.n4.3}, url = {http://global-sci.org/intro/article_detail/jpde/5119.html} }
TY - JOUR T1 - Semi-discretization Difference Approximation for a Cauchy Problem of Heat Equation in Two-dimensional Space AU - Xiong , Xiangtuan AU - Li , Jinmei JO - Journal of Partial Differential Equations VL - 4 SP - 315 EP - 331 PY - 2015 DA - 2015/12 SN - 28 DO - http://doi.org/10.4208/jpde.v28.n4.3 UR - https://global-sci.org/intro/article_detail/jpde/5119.html KW - 2D inverse heat conduction problem KW - Ill-posedness KW - regularization KW - error estimate KW - finite difference AB - In this paper we consider a semi-descretization difference scheme for solving a Cauchy problem of heat equation in two-dimensional setting. Some error estimates are proved for the semi-descretization difference regularization method which cannot be fitted into the framework of regularization theory presented by Engl, Hanke and Neubauer. Numerical results show that the proposed method works well.
Xiangtuan Xiong & Jinmei Li. (2019). Semi-discretization Difference Approximation for a Cauchy Problem of Heat Equation in Two-dimensional Space. Journal of Partial Differential Equations. 28 (4). 315-331. doi:10.4208/jpde.v28.n4.3
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