Identification of a time-dependent perfusion coefficient in a 2D bioheat equation with mixed Dirichlet-Wentzell boundary conditions

Date

2026-10-01

Author

Ismailov, Mansur I.
Türk, Önder

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We investigate an inverse coefficient problem for the two-dimensional heat equation on rectangular domains subject to a non-classical boundary condition. Specifically, a Wentzell (dynamic) boundary condition is imposed on a portion of the boundary, and absorption is specified on the remaining part leading to mixed Dirichlet-Wentzell boundary conditions. The inverse task is to recover a time-dependent coefficient in the zeroth-order term, representing perfusion-mediated volumetric heat exchange, from prescribed integral (energy-type) observations. Exploiting the rectangular geometry, we develop a Fourier series framework built upon an auxiliary spectral problem in which the eigenparameter appears both in the differential operator and in the boundary conditions. Under appropriate regularity, compatibility, orthogonality, and identifiability assumptions, we establish well-posedness of the forward and inverse formulations, and derive stability properties that support numerical reconstruction. We then demonstrate computational feasibility by combining complementary numerical schemes featuring different approximation characteristics for the associated eigenvalue problem and for the inverse reconstruction. Numerical experiments corroborate the theoretical results and exhibit very good agreement with reference solutions.

URI

https://hdl.handle.net/11511/120763

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Graduate School of Applied Mathematics, Article