Quasi solution of a backward space fractional diffusion equation
In this paper, based on a quasi solution approach, i.e., a methodology involving minimization of a least squares cost functional, we study a backward space fractional diffusion equation. To this end, we give existence and uniqueness theorems of a quasi solution in an appropriate class of admissible...
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| Published in | Journal of inverse and ill-posed problems Vol. 27; no. 6; pp. 795 - 814 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin
De Gruyter
01.12.2019
Walter de Gruyter GmbH |
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| Abstract | In this paper, based on a quasi solution approach, i.e., a methodology involving minimization of a least squares cost functional, we study a backward space fractional diffusion equation.
To this end, we give existence and uniqueness theorems of a quasi solution in an appropriate class of admissible initial data.
In addition, in order to approximate the quasi solution, the finite element method is used.
Since the obtained system of linear equations is ill-posed, we apply TSVD regularization.
Finally, three numerical examples are given.
Numerical results reveal the efficiency and applicability of the proposed method. |
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| AbstractList | In this paper, based on a quasi solution approach, i.e., a methodology involving minimization of a least squares cost functional, we study a backward space fractional diffusion equation.
To this end, we give existence and uniqueness theorems of a quasi solution in an appropriate class of admissible initial data.
In addition, in order to approximate the quasi solution, the finite element method is used.
Since the obtained system of linear equations is ill-posed, we apply TSVD regularization.
Finally, three numerical examples are given.
Numerical results reveal the efficiency and applicability of the proposed method. In this paper, based on a quasi solution approach, i.e., a methodology involving minimization of a least squares cost functional, we study a backward space fractional diffusion equation. To this end, we give existence and uniqueness theorems of a quasi solution in an appropriate class of admissible initial data. In addition, in order to approximate the quasi solution, the finite element method is used. Since the obtained system of linear equations is ill-posed, we apply TSVD regularization. Finally, three numerical examples are given. Numerical results reveal the efficiency and applicability of the proposed method. |
| Author | Zakeri, Ali Salehi Shayegan, Amir Hossein |
| Author_xml | – sequence: 1 givenname: Amir Hossein surname: Salehi Shayegan fullname: Salehi Shayegan, Amir Hossein email: ah.salehi@mail.kntu.ac.ir organization: Faculty of Mathematics, K. N. Toosi University of Technology, Tehran, Iran – sequence: 2 givenname: Ali surname: Zakeri fullname: Zakeri, Ali email: azakeri@kntu.ac.ir organization: Faculty of Mathematics, K. N. Toosi University of Technology, Tehran, Iran |
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| Cites_doi | 10.1080/17415977.2017.1384826 10.1007/s11075-015-0065-8 10.1016/j.amc.2005.11.114 10.1007/s10444-004-1811-y 10.1137/S0036142994276785 10.1137/080714130 10.1088/0266-5611/20/2/019 10.4208/cicp.020709.221209a 10.1016/j.jmaa.2006.08.040 10.1515/jip-2011-0021 10.1016/j.apm.2013.03.071 10.1080/10682760410001710141 10.1016/S0168-9274(00)00025-8 10.1016/j.camwa.2015.11.023 10.1155/2012/596184 10.1080/00036810903479731 10.3934/ipi.2018033 10.1007/BF01937276 10.1016/j.aml.2007.06.007 10.2478/s13540-011-0028-2 10.1137/1034115 10.1002/num.20112 10.1002/mma.4284 10.1016/j.trmi.2017.05.003 10.1007/s002110050073 |
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| SubjectTerms | 35R11 65N21 Backward space fractional diffusion equation Existence theorems Finite element method Ill posed problems Linear equations quasi solution Regularization stability TSVD regularization Uniqueness theorems |
| Title | Quasi solution of a backward space fractional diffusion equation |
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