Quasi solution of a backward space fractional diffusion equation
2019 ◽
Vol 27
(6)
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pp. 795-814
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Keyword(s):
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.
2014 ◽
Vol 2014
(1)
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pp. 231
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2017 ◽
Vol 26
(7)
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pp. 925-941
2013 ◽
Vol 2013
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pp. 1-8
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2013 ◽
Vol 21
(9)
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pp. 1769-1777
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2018 ◽
Vol 148
◽
pp. 37-47
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