| Abstract: |
| In this work, we investigate the inverse problem of determining a semilinear term appearing in a nonlinear parabolic equation from the measurement of the conormal derivative on the boundary. We first establish a uniqueness result, showing that the nonlinear term is uniquely determined provided the difference between two candidates does not change sign infinitely many times. Subsequently, we derive H\older-type stability estimates for the reconstruction, where the stability exponent depends explicitly on the number of sign changes of the difference between two admissible nonlinear terms. Improved stability estimates are obtained under higher regularity assumptions on the nonlinear term. Finally, we propose a numerical reconstruction algorithm based on an iterative scheme and validate its performance through various numerical experiments with noisy data. |
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