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Inverse Source Problem for a Singular Parabolic Equation with Variable Coefficients

Author

Listed:
  • Xue Qin

    (School of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Hefei 233030, China)

  • Shumin Li

    (School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China)

Abstract

We consider a parabolic equation with a singular potential in a bounded domain Ω ⊂ R n . The main result is a Lipschitz stability estimate for an inverse source problem of determining a spatial varying factor f ( x ) of the source term R ( x , t ) f ( x ) . We obtain a consistent stability result for any μ ≤ p 1 μ * , where p 1 > 0 is the lower bound of p ( x ) and μ * = ( n − 2 ) 2 / 4 , and this condition for μ is also almost a consistently optimal condition for the existence of solutions. The main method we used is the Carleman estimate, and the proof for the inverse source problem relies on the Bukhgeim–Klibanov method.

Suggested Citation

  • Xue Qin & Shumin Li, 2025. "Inverse Source Problem for a Singular Parabolic Equation with Variable Coefficients," Mathematics, MDPI, vol. 13(10), pages 1-22, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:10:p:1678-:d:1660103
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