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Award ID contains: 2451193

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  1. ; (, Inverse Problems)
    Abstract This paper proposes a computational method to reconstruct both the birth and mortality coefficients in an age-structured population diffusive model. In mathematical oncology, solving this inverse problem is crucial for assessing the effectiveness of anti-cancer treatments and thus, gaining insights into the post-treatment dynamics of tumors. Through some linear and nonlinear transformations, the targeted inverse model is transformed into an auxiliary third-order nonlinear PDE. Subsequently, a coupled age-dependent quasi-linear parabolic PDE system is derived using the Fourier–Klibanov basis. The resulting PDE system is then approximated through the minimization of a cost functional, weighted by a suitable Carleman function. Ultimately, an analysis of the minimization problem is studied through a new Carleman estimate, and some computational results are presented to show how the proposed method works. 
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  2. ; (, Journal of Computational Physics)
    Free, publicly-accessible full text available October 1, 2026
  3. ; (, Communications on Analysis and Computation)
    Free, publicly-accessible full text available September 18, 2026
  4. ; ; ; (, Journal of Computational Science)
    Full Text Available