A truncation regularization method for a time fractional diffusion equation with an in-homogeneous source
In the present paper, we consider a time-fractional inverse diffusion problem with an in-homogeneous source, where data is given at x = 1 and the solution is required in the interval 0 < x < 1. This problem is ill-posed, i.e. the solution (if it exists) does not depend continuously on the data...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
EDP Sciences
2018-01-01
|
| Series: | ITM Web of Conferences |
| Subjects: | |
| Online Access: | https://doi.org/10.1051/itmconf/20182002007 |
| _version_ | 1818854916536401920 |
|---|---|
| author | Vu Cam Hoan Luu Duy Binh Ho Bao Ngoc Tran |
| author_facet | Vu Cam Hoan Luu Duy Binh Ho Bao Ngoc Tran |
| author_sort | Vu Cam Hoan Luu |
| collection | DOAJ |
| description | In the present paper, we consider a time-fractional inverse diffusion problem with an in-homogeneous source, where data is given at x = 1 and the solution is required in the interval 0 < x < 1. This problem is ill-posed, i.e. the solution (if it exists) does not depend continuously on the data. We propose a regularization method to solve it based on the solution given by the Fourier method. |
| first_indexed | 2024-12-19T08:00:19Z |
| format | Article |
| id | doaj.art-c6f600df425244d5b74e9256e02927a0 |
| institution | Directory Open Access Journal |
| issn | 2271-2097 |
| language | English |
| last_indexed | 2024-12-19T08:00:19Z |
| publishDate | 2018-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | ITM Web of Conferences |
| spelling | doaj.art-c6f600df425244d5b74e9256e02927a02022-12-21T20:29:53ZengEDP SciencesITM Web of Conferences2271-20972018-01-01200200710.1051/itmconf/20182002007itmconf_icm2018_02007A truncation regularization method for a time fractional diffusion equation with an in-homogeneous sourceVu Cam Hoan LuuDuy Binh HoBao Ngoc TranIn the present paper, we consider a time-fractional inverse diffusion problem with an in-homogeneous source, where data is given at x = 1 and the solution is required in the interval 0 < x < 1. This problem is ill-posed, i.e. the solution (if it exists) does not depend continuously on the data. We propose a regularization method to solve it based on the solution given by the Fourier method.https://doi.org/10.1051/itmconf/20182002007Ill-posed problemtime fractional diffusion equationregularizationregularized truncation method |
| spellingShingle | Vu Cam Hoan Luu Duy Binh Ho Bao Ngoc Tran A truncation regularization method for a time fractional diffusion equation with an in-homogeneous source ITM Web of Conferences Ill-posed problem time fractional diffusion equation regularization regularized truncation method |
| title | A truncation regularization method for a time fractional diffusion equation with an in-homogeneous source |
| title_full | A truncation regularization method for a time fractional diffusion equation with an in-homogeneous source |
| title_fullStr | A truncation regularization method for a time fractional diffusion equation with an in-homogeneous source |
| title_full_unstemmed | A truncation regularization method for a time fractional diffusion equation with an in-homogeneous source |
| title_short | A truncation regularization method for a time fractional diffusion equation with an in-homogeneous source |
| title_sort | truncation regularization method for a time fractional diffusion equation with an in homogeneous source |
| topic | Ill-posed problem time fractional diffusion equation regularization regularized truncation method |
| url | https://doi.org/10.1051/itmconf/20182002007 |
| work_keys_str_mv | AT vucamhoanluu atruncationregularizationmethodforatimefractionaldiffusionequationwithaninhomogeneoussource AT duybinhho atruncationregularizationmethodforatimefractionaldiffusionequationwithaninhomogeneoussource AT baongoctran atruncationregularizationmethodforatimefractionaldiffusionequationwithaninhomogeneoussource AT vucamhoanluu truncationregularizationmethodforatimefractionaldiffusionequationwithaninhomogeneoussource AT duybinhho truncationregularizationmethodforatimefractionaldiffusionequationwithaninhomogeneoussource AT baongoctran truncationregularizationmethodforatimefractionaldiffusionequationwithaninhomogeneoussource |