| Abstract: |
| We consider the asymptotic behavior of the heat content associated with polyharmonic heat equations as time approaches zero.
Here, the heat content is defined as the mass of solutions over a fixed smooth compact set with initial data given by the indicator function of this set.
More precisely, we derive a higher-order asymptotic expansion of the heat content and provide explicit expressions for the coefficients, which reflect the geometric properties of the boundary.
We also discuss a connection between our results and a thresholding algorithm for a geometric evolution equation. |
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