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An investigation of an inverse problem for second-order abstract differential equation

Author

Listed:
  • Muslim Malik

    (Indian Institute of Technology Mandi)

  • Santosh Ruhil

    (Indian Institute of Technology Mandi)

  • Rajesh Dhayal

    (Thapar Institute of Engineering and Technology)

Abstract

In this manuscript, we consider an inverse problem for a second-order abstract differential equation in a Banach space and identify the parameter using an over-determined condition on a mild solution. A direct approach using Volterra integral equation for sufficiently regular data and an optimal control approach for less regular data are the main techniques to find the solution pair of the considered problem. Finally, an application to an inverse problem that appears in elasticity theory is presented.

Suggested Citation

  • Muslim Malik & Santosh Ruhil & Rajesh Dhayal, 2025. "An investigation of an inverse problem for second-order abstract differential equation," Indian Journal of Pure and Applied Mathematics, Springer, vol. 56(2), pages 512-525, June.
    • Handle: RePEc:spr:indpam:v:56:y:2025:i:2:d:10.1007_s13226-023-00498-9
    DOI: 10.1007/s13226-023-00498-9
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