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

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  • Chunlong Sun
  • Qian Liu
  • Gongsheng Li

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.

Suggested Citation

  • Chunlong Sun & Qian Liu & Gongsheng Li, 2017. "Conditional Well-Posedness for an Inverse Source Problem in the Diffusion Equation Using the Variational Adjoint Method," Advances in Mathematical Physics, Hindawi, vol. 2017, pages 1-6, June.
    • Handle: RePEc:hin:jnlamp:6801260
    DOI: 10.1155/2017/6801260
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    Cited by:

    1. Jaan Janno, 2023. "Inverse Problem to Determine Two Time-Dependent Source Factors of Fractional Diffusion-Wave Equations from Final Data and Simultaneous Reconstruction of Location and Time History of a Point Source," Mathematics, MDPI, vol. 11(2), pages 1-17, January.

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