Conditional Well-Posedness for an Inverse Source Problem in the Diffusion Equation Using the Variational Adjoint Method
Joint Authors
Li, Gongsheng
Sun, Chunlong
Liu, Qian
Source
Advances in Mathematical Physics
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-6, 6 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-06-27
Country of Publication
Egypt
No. of Pages
6
Main Subjects
Abstract EN
This article deals with an inverse problem of determining a linear source term in the multidimensional diffusion equation using the variational adjoint method.
A variational identity connecting the known data with the unknown is established based on an adjoint problem, and a conditional uniqueness for the inverse source problem is proved by the approximate controllability to the adjoint problem under the condition that the unknowns can keep orders locally.
Furthermore, a bilinear form is set forth also based on the variational identity and then a norm for the unknowns is well-defined by which a conditional Lipschitz stability is established.
American Psychological Association (APA)
Sun, Chunlong& Liu, Qian& Li, Gongsheng. 2017. Conditional Well-Posedness for an Inverse Source Problem in the Diffusion Equation Using the Variational Adjoint Method. Advances in Mathematical Physics،Vol. 2017, no. 2017, pp.1-6.
https://search.emarefa.net/detail/BIM-1123261
Modern Language Association (MLA)
Sun, Chunlong…[et al.]. Conditional Well-Posedness for an Inverse Source Problem in the Diffusion Equation Using the Variational Adjoint Method. Advances in Mathematical Physics No. 2017 (2017), pp.1-6.
https://search.emarefa.net/detail/BIM-1123261
American Medical Association (AMA)
Sun, Chunlong& Liu, Qian& Li, Gongsheng. Conditional Well-Posedness for an Inverse Source Problem in the Diffusion Equation Using the Variational Adjoint Method. Advances in Mathematical Physics. 2017. Vol. 2017, no. 2017, pp.1-6.
https://search.emarefa.net/detail/BIM-1123261
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1123261