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This work demonstrates the bubble tree decomposition contains one bubble in harmonic map heat flow, indicating complex behaviors under boundary conditions.
We consider finite-time and k-equivariant solutions to the harmonic map heat flow from B² to S² under general time-dependent boundary data and prove that the bubble tree decomposition contains only one bubble. The method relies on the Maximum and Comparison Principle. We also exhibit solutions blowing up in infinite time for any k ≥ 1.
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Dylan Samuelian (2025) studied this question.
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