Conditional Well‐Posedness for an Inverse Source Problem in the Diffusion Equation Using the Variational Adjoint Method

Chunlong Sun, Qian Liu and Gongsheng Li

Advances in Mathematical Physics, 2017, vol. 2017, issue 1

Abstract: 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.

Date: 2017
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2017/6801260

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2017:y:2017:i:1:n:6801260

Access Statistics for this article

More articles in Advances in Mathematical Physics from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().