Inverse Estimates for Nonhomogeneous Backward Heat Problems
We investigate the inverse problem in the nonhomogeneous heat equation involving the recovery of the initial temperature from measurements of the final temperature. This problem is known as the backward heat problem and is severely ill-posed. We show that this problem can be converted into the first...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/529618 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832568299312906240 |
|---|---|
| author | Tao Min Weimin Fu Qiang Huang |
| author_facet | Tao Min Weimin Fu Qiang Huang |
| author_sort | Tao Min |
| collection | DOAJ |
| description | We investigate the inverse problem in the nonhomogeneous heat equation involving the recovery of the initial temperature from measurements of the final temperature. This problem is known as the backward heat problem and is severely ill-posed. We show that this problem can be converted into the first Fredholm integral equation, and an algorithm of inversion is given using Tikhonov's regularization method. The genetic algorithm for obtaining the regularization parameter is presented. We also present numerical computations that verify the accuracy of our approximation. |
| format | Article |
| id | doaj-art-80f586f8e9a047e781dcf462f8d69ca7 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-80f586f8e9a047e781dcf462f8d69ca72025-02-03T00:59:22ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/529618529618Inverse Estimates for Nonhomogeneous Backward Heat ProblemsTao Min0Weimin Fu1Qiang Huang2School of Science, Xi'an University of Technology, Xi'an, Shaanxi 710054, ChinaSchool of Science, Xi'an University of Technology, Xi'an, Shaanxi 710054, ChinaState Key Laboratory of Eco-Hydraulic Engineering in Shaanxi, Xi'an University of Technology, Xi'an, Shaanxi 710048, ChinaWe investigate the inverse problem in the nonhomogeneous heat equation involving the recovery of the initial temperature from measurements of the final temperature. This problem is known as the backward heat problem and is severely ill-posed. We show that this problem can be converted into the first Fredholm integral equation, and an algorithm of inversion is given using Tikhonov's regularization method. The genetic algorithm for obtaining the regularization parameter is presented. We also present numerical computations that verify the accuracy of our approximation.http://dx.doi.org/10.1155/2014/529618 |
| spellingShingle | Tao Min Weimin Fu Qiang Huang Inverse Estimates for Nonhomogeneous Backward Heat Problems Journal of Applied Mathematics |
| title | Inverse Estimates for Nonhomogeneous Backward Heat Problems |
| title_full | Inverse Estimates for Nonhomogeneous Backward Heat Problems |
| title_fullStr | Inverse Estimates for Nonhomogeneous Backward Heat Problems |
| title_full_unstemmed | Inverse Estimates for Nonhomogeneous Backward Heat Problems |
| title_short | Inverse Estimates for Nonhomogeneous Backward Heat Problems |
| title_sort | inverse estimates for nonhomogeneous backward heat problems |
| url | http://dx.doi.org/10.1155/2014/529618 |
| work_keys_str_mv | AT taomin inverseestimatesfornonhomogeneousbackwardheatproblems AT weiminfu inverseestimatesfornonhomogeneousbackwardheatproblems AT qianghuang inverseestimatesfornonhomogeneousbackwardheatproblems |