| Abstract: |
| This talk addresses the inverse problem of simultaneously identifying a piecewise-constant reaction coefficient and the initial condition in a one-dimensional reaction--diffusion equation, using only boundary control and observation data. We propose a novel ON/OFF control strategy combined with an estimation/cancellation mechanism. This approach decomposes the problem of simultaneous identifiability into two sequential subproblems: first, uniquely determining the reaction coefficient; second, reconstructing the initial value. By applying Property C, we establish the unique identifiability of the piecewise-constant reaction coefficient. The initial value is then recovered via spectral analysis. A key advantage of our framework is its exclusive reliance on boundary data, eliminating the need for interior measurements and thereby enhancing practical applicability. |
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