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, 1-6

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
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlamp:6801260

DOI: 10.1155/2017/6801260

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