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The aim is to recover a space/time heat source from the temperature distribution governed by the polyharmonic heat equation.

Inverse source problems for the polyharmonic heat equation

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The aim is to recover a space/time heat source from the temperature distribution governed by the polyharmonic heat equation.
Utilized values of temperature and its normal derivatives on the cylinder's lateral surface.
Applied initial value and time-averaged data for space-dependent sources.
Used space-averaged data for time-dependent sources.
Proved well-posedness through series expansion in terms of eigenfunctions.
Identified that k=[d/4l]+2 is admissible for data regularity.
Established the well-posedness of the solution for the inverse problem using eigenvalue inequalities.

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This investigation recovers heat sources in polyharmonic heat equations, suggesting new methods for thermal modeling.

Ismailov et al. (2026) studied this question.

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